We consider the following Problem:

  Strict Trs:
    {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
     , active(__(X, nil())) -> mark(X)
     , active(__(nil(), X)) -> mark(X)
     , active(and(tt(), X)) -> mark(X)
     , active(isNePal(__(I, __(P, I)))) -> mark(tt())
     , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
     , mark(nil()) -> active(nil())
     , mark(and(X1, X2)) -> active(and(mark(X1), X2))
     , mark(tt()) -> active(tt())
     , mark(isNePal(X)) -> active(isNePal(mark(X)))
     , __(mark(X1), X2) -> __(X1, X2)
     , __(X1, mark(X2)) -> __(X1, X2)
     , __(active(X1), X2) -> __(X1, X2)
     , __(X1, active(X2)) -> __(X1, X2)
     , and(mark(X1), X2) -> and(X1, X2)
     , and(X1, mark(X2)) -> and(X1, X2)
     , and(active(X1), X2) -> and(X1, X2)
     , and(X1, active(X2)) -> and(X1, X2)
     , isNePal(mark(X)) -> isNePal(X)
     , isNePal(active(X)) -> isNePal(X)}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
       , active(__(X, nil())) -> mark(X)
       , active(__(nil(), X)) -> mark(X)
       , active(and(tt(), X)) -> mark(X)
       , active(isNePal(__(I, __(P, I)))) -> mark(tt())
       , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
       , mark(nil()) -> active(nil())
       , mark(and(X1, X2)) -> active(and(mark(X1), X2))
       , mark(tt()) -> active(tt())
       , mark(isNePal(X)) -> active(isNePal(mark(X)))
       , __(mark(X1), X2) -> __(X1, X2)
       , __(X1, mark(X2)) -> __(X1, X2)
       , __(active(X1), X2) -> __(X1, X2)
       , __(X1, active(X2)) -> __(X1, X2)
       , and(mark(X1), X2) -> and(X1, X2)
       , and(X1, mark(X2)) -> and(X1, X2)
       , and(active(X1), X2) -> and(X1, X2)
       , and(X1, active(X2)) -> and(X1, X2)
       , isNePal(mark(X)) -> isNePal(X)
       , isNePal(active(X)) -> isNePal(X)}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  __(mark(X1), X2) -> __(X1, X2)
       , __(active(X1), X2) -> __(X1, X2)
       , __(X1, active(X2)) -> __(X1, X2)
       , and(mark(X1), X2) -> and(X1, X2)
       , and(X1, mark(X2)) -> and(X1, X2)
       , and(active(X1), X2) -> and(X1, X2)
       , and(X1, active(X2)) -> and(X1, X2)
       , isNePal(mark(X)) -> isNePal(X)
       , isNePal(active(X)) -> isNePal(X)}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
        Uargs(and) = {1}, Uargs(isNePal) = {1}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       active(x1) = [1 0] x1 + [1]
                    [0 1]      [1]
       __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                    [0 0]      [0 1]      [0]
       mark(x1) = [1 0] x1 + [1]
                  [1 0]      [1]
       nil() = [0]
               [0]
       and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                     [0 0]      [0 0]      [0]
       tt() = [0]
              [0]
       isNePal(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:
        {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
         , active(__(X, nil())) -> mark(X)
         , active(__(nil(), X)) -> mark(X)
         , active(and(tt(), X)) -> mark(X)
         , active(isNePal(__(I, __(P, I)))) -> mark(tt())
         , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
         , mark(nil()) -> active(nil())
         , mark(and(X1, X2)) -> active(and(mark(X1), X2))
         , mark(tt()) -> active(tt())
         , mark(isNePal(X)) -> active(isNePal(mark(X)))
         , __(X1, mark(X2)) -> __(X1, X2)}
      Weak Trs:
        {  __(mark(X1), X2) -> __(X1, X2)
         , __(active(X1), X2) -> __(X1, X2)
         , __(X1, active(X2)) -> __(X1, X2)
         , and(mark(X1), X2) -> and(X1, X2)
         , and(X1, mark(X2)) -> and(X1, X2)
         , and(active(X1), X2) -> and(X1, X2)
         , and(X1, active(X2)) -> and(X1, X2)
         , isNePal(mark(X)) -> isNePal(X)
         , isNePal(active(X)) -> isNePal(X)}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      The weightgap principle applies, where following rules are oriented strictly:
      
      TRS Component: {__(X1, mark(X2)) -> __(X1, X2)}
      
      Interpretation of nonconstant growth:
      -------------------------------------
        The following argument positions are usable:
          Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
          Uargs(and) = {1}, Uargs(isNePal) = {1}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         active(x1) = [1 0] x1 + [1]
                      [0 0]      [1]
         __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                      [0 0]      [0 0]      [1]
         mark(x1) = [1 0] x1 + [1]
                    [0 0]      [1]
         nil() = [0]
                 [0]
         and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                       [0 0]      [0 0]      [1]
         tt() = [0]
                [0]
         isNePal(x1) = [1 0] x1 + [0]
                       [0 0]      [1]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
           , active(__(X, nil())) -> mark(X)
           , active(__(nil(), X)) -> mark(X)
           , active(and(tt(), X)) -> mark(X)
           , active(isNePal(__(I, __(P, I)))) -> mark(tt())
           , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
           , mark(nil()) -> active(nil())
           , mark(and(X1, X2)) -> active(and(mark(X1), X2))
           , mark(tt()) -> active(tt())
           , mark(isNePal(X)) -> active(isNePal(mark(X)))}
        Weak Trs:
          {  __(X1, mark(X2)) -> __(X1, X2)
           , __(mark(X1), X2) -> __(X1, X2)
           , __(active(X1), X2) -> __(X1, X2)
           , __(X1, active(X2)) -> __(X1, X2)
           , and(mark(X1), X2) -> and(X1, X2)
           , and(X1, mark(X2)) -> and(X1, X2)
           , and(active(X1), X2) -> and(X1, X2)
           , and(X1, active(X2)) -> and(X1, X2)
           , isNePal(mark(X)) -> isNePal(X)
           , isNePal(active(X)) -> isNePal(X)}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^1))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component:
          {  active(and(tt(), X)) -> mark(X)
           , active(isNePal(__(I, __(P, I)))) -> mark(tt())}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
            Uargs(and) = {1}, Uargs(isNePal) = {1}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           active(x1) = [1 2] x1 + [1]
                        [0 0]      [1]
           __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                        [0 0]      [0 0]      [0]
           mark(x1) = [1 0] x1 + [1]
                      [0 0]      [1]
           nil() = [0]
                   [0]
           and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                         [0 0]      [0 0]      [3]
           tt() = [0]
                  [0]
           isNePal(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:
            {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
             , active(__(X, nil())) -> mark(X)
             , active(__(nil(), X)) -> mark(X)
             , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
             , mark(nil()) -> active(nil())
             , mark(and(X1, X2)) -> active(and(mark(X1), X2))
             , mark(tt()) -> active(tt())
             , mark(isNePal(X)) -> active(isNePal(mark(X)))}
          Weak Trs:
            {  active(and(tt(), X)) -> mark(X)
             , active(isNePal(__(I, __(P, I)))) -> mark(tt())
             , __(X1, mark(X2)) -> __(X1, X2)
             , __(mark(X1), X2) -> __(X1, X2)
             , __(active(X1), X2) -> __(X1, X2)
             , __(X1, active(X2)) -> __(X1, X2)
             , and(mark(X1), X2) -> and(X1, X2)
             , and(X1, mark(X2)) -> and(X1, X2)
             , and(active(X1), X2) -> and(X1, X2)
             , and(X1, active(X2)) -> and(X1, X2)
             , isNePal(mark(X)) -> isNePal(X)
             , isNePal(active(X)) -> isNePal(X)}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^1))
        
        Proof:
          The weightgap principle applies, where following rules are oriented strictly:
          
          TRS Component:
            {  active(__(X, nil())) -> mark(X)
             , active(__(nil(), X)) -> mark(X)}
          
          Interpretation of nonconstant growth:
          -------------------------------------
            The following argument positions are usable:
              Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
              Uargs(and) = {1}, Uargs(isNePal) = {1}
            We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
            Interpretation Functions:
             active(x1) = [1 1] x1 + [1]
                          [0 0]      [0]
             __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                          [0 0]      [0 0]      [0]
             mark(x1) = [1 0] x1 + [1]
                        [0 0]      [0]
             nil() = [2]
                     [2]
             and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                           [0 0]      [0 0]      [0]
             tt() = [0]
                    [0]
             isNePal(x1) = [1 0] x1 + [0]
                           [0 0]      [3]
          
          The strictly oriented rules are moved into the weak component.
          
          We consider the following Problem:
          
            Strict Trs:
              {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
               , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
               , mark(nil()) -> active(nil())
               , mark(and(X1, X2)) -> active(and(mark(X1), X2))
               , mark(tt()) -> active(tt())
               , mark(isNePal(X)) -> active(isNePal(mark(X)))}
            Weak Trs:
              {  active(__(X, nil())) -> mark(X)
               , active(__(nil(), X)) -> mark(X)
               , active(and(tt(), X)) -> mark(X)
               , active(isNePal(__(I, __(P, I)))) -> mark(tt())
               , __(X1, mark(X2)) -> __(X1, X2)
               , __(mark(X1), X2) -> __(X1, X2)
               , __(active(X1), X2) -> __(X1, X2)
               , __(X1, active(X2)) -> __(X1, X2)
               , and(mark(X1), X2) -> and(X1, X2)
               , and(X1, mark(X2)) -> and(X1, X2)
               , and(active(X1), X2) -> and(X1, X2)
               , and(X1, active(X2)) -> and(X1, X2)
               , isNePal(mark(X)) -> isNePal(X)
               , isNePal(active(X)) -> isNePal(X)}
            StartTerms: basic terms
            Strategy: innermost
          
          Certificate: YES(?,O(n^1))
          
          Proof:
            The weightgap principle applies, where following rules are oriented strictly:
            
            TRS Component: {mark(tt()) -> active(tt())}
            
            Interpretation of nonconstant growth:
            -------------------------------------
              The following argument positions are usable:
                Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
                Uargs(and) = {1}, Uargs(isNePal) = {1}
              We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
              Interpretation Functions:
               active(x1) = [1 0] x1 + [0]
                            [0 1]      [3]
               __(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                            [1 1]      [1 1]      [2]
               mark(x1) = [1 0] x1 + [1]
                          [1 1]      [0]
               nil() = [0]
                       [1]
               and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                             [1 1]      [1 1]      [0]
               tt() = [3]
                      [0]
               isNePal(x1) = [1 0] x1 + [3]
                             [0 1]      [0]
            
            The strictly oriented rules are moved into the weak component.
            
            We consider the following Problem:
            
              Strict Trs:
                {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
                 , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
                 , mark(nil()) -> active(nil())
                 , mark(and(X1, X2)) -> active(and(mark(X1), X2))
                 , mark(isNePal(X)) -> active(isNePal(mark(X)))}
              Weak Trs:
                {  mark(tt()) -> active(tt())
                 , active(__(X, nil())) -> mark(X)
                 , active(__(nil(), X)) -> mark(X)
                 , active(and(tt(), X)) -> mark(X)
                 , active(isNePal(__(I, __(P, I)))) -> mark(tt())
                 , __(X1, mark(X2)) -> __(X1, X2)
                 , __(mark(X1), X2) -> __(X1, X2)
                 , __(active(X1), X2) -> __(X1, X2)
                 , __(X1, active(X2)) -> __(X1, X2)
                 , and(mark(X1), X2) -> and(X1, X2)
                 , and(X1, mark(X2)) -> and(X1, X2)
                 , and(active(X1), X2) -> and(X1, X2)
                 , and(X1, active(X2)) -> and(X1, X2)
                 , isNePal(mark(X)) -> isNePal(X)
                 , isNePal(active(X)) -> isNePal(X)}
              StartTerms: basic terms
              Strategy: innermost
            
            Certificate: YES(?,O(n^1))
            
            Proof:
              The weightgap principle applies, where following rules are oriented strictly:
              
              TRS Component: {mark(nil()) -> active(nil())}
              
              Interpretation of nonconstant growth:
              -------------------------------------
                The following argument positions are usable:
                  Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
                  Uargs(and) = {1}, Uargs(isNePal) = {1}
                We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                Interpretation Functions:
                 active(x1) = [1 1] x1 + [1]
                              [0 0]      [1]
                 __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 0]      [0 0]      [0]
                 mark(x1) = [1 0] x1 + [3]
                            [0 0]      [1]
                 nil() = [2]
                         [1]
                 and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                               [0 0]      [0 0]      [0]
                 tt() = [2]
                        [0]
                 isNePal(x1) = [1 0] x1 + [3]
                               [0 0]      [1]
              
              The strictly oriented rules are moved into the weak component.
              
              We consider the following Problem:
              
                Strict Trs:
                  {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
                   , mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
                   , mark(and(X1, X2)) -> active(and(mark(X1), X2))
                   , mark(isNePal(X)) -> active(isNePal(mark(X)))}
                Weak Trs:
                  {  mark(nil()) -> active(nil())
                   , mark(tt()) -> active(tt())
                   , active(__(X, nil())) -> mark(X)
                   , active(__(nil(), X)) -> mark(X)
                   , active(and(tt(), X)) -> mark(X)
                   , active(isNePal(__(I, __(P, I)))) -> mark(tt())
                   , __(X1, mark(X2)) -> __(X1, X2)
                   , __(mark(X1), X2) -> __(X1, X2)
                   , __(active(X1), X2) -> __(X1, X2)
                   , __(X1, active(X2)) -> __(X1, X2)
                   , and(mark(X1), X2) -> and(X1, X2)
                   , and(X1, mark(X2)) -> and(X1, X2)
                   , and(active(X1), X2) -> and(X1, X2)
                   , and(X1, active(X2)) -> and(X1, X2)
                   , isNePal(mark(X)) -> isNePal(X)
                   , isNePal(active(X)) -> isNePal(X)}
                StartTerms: basic terms
                Strategy: innermost
              
              Certificate: YES(?,O(n^1))
              
              Proof:
                The weightgap principle applies, where following rules are oriented strictly:
                
                TRS Component: {active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))}
                
                Interpretation of nonconstant growth:
                -------------------------------------
                  The following argument positions are usable:
                    Uargs(active) = {1}, Uargs(__) = {1, 2}, Uargs(mark) = {1},
                    Uargs(and) = {1}, Uargs(isNePal) = {1}
                  We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                  Interpretation Functions:
                   active(x1) = [1 2] x1 + [0]
                                [0 0]      [0]
                   __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                [0 0]      [0 0]      [2]
                   mark(x1) = [1 0] x1 + [0]
                              [0 0]      [0]
                   nil() = [0]
                           [0]
                   and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                 [0 0]      [0 0]      [0]
                   tt() = [0]
                          [0]
                   isNePal(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:
                    {  mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
                     , mark(and(X1, X2)) -> active(and(mark(X1), X2))
                     , mark(isNePal(X)) -> active(isNePal(mark(X)))}
                  Weak Trs:
                    {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
                     , mark(nil()) -> active(nil())
                     , mark(tt()) -> active(tt())
                     , active(__(X, nil())) -> mark(X)
                     , active(__(nil(), X)) -> mark(X)
                     , active(and(tt(), X)) -> mark(X)
                     , active(isNePal(__(I, __(P, I)))) -> mark(tt())
                     , __(X1, mark(X2)) -> __(X1, X2)
                     , __(mark(X1), X2) -> __(X1, X2)
                     , __(active(X1), X2) -> __(X1, X2)
                     , __(X1, active(X2)) -> __(X1, X2)
                     , and(mark(X1), X2) -> and(X1, X2)
                     , and(X1, mark(X2)) -> and(X1, X2)
                     , and(active(X1), X2) -> and(X1, X2)
                     , and(X1, active(X2)) -> and(X1, X2)
                     , isNePal(mark(X)) -> isNePal(X)
                     , isNePal(active(X)) -> isNePal(X)}
                  StartTerms: basic terms
                  Strategy: innermost
                
                Certificate: YES(?,O(n^1))
                
                Proof:
                  We consider the following Problem:
                  
                    Strict Trs:
                      {  mark(__(X1, X2)) -> active(__(mark(X1), mark(X2)))
                       , mark(and(X1, X2)) -> active(and(mark(X1), X2))
                       , mark(isNePal(X)) -> active(isNePal(mark(X)))}
                    Weak Trs:
                      {  active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
                       , mark(nil()) -> active(nil())
                       , mark(tt()) -> active(tt())
                       , active(__(X, nil())) -> mark(X)
                       , active(__(nil(), X)) -> mark(X)
                       , active(and(tt(), X)) -> mark(X)
                       , active(isNePal(__(I, __(P, I)))) -> mark(tt())
                       , __(X1, mark(X2)) -> __(X1, X2)
                       , __(mark(X1), X2) -> __(X1, X2)
                       , __(active(X1), X2) -> __(X1, X2)
                       , __(X1, active(X2)) -> __(X1, X2)
                       , and(mark(X1), X2) -> and(X1, X2)
                       , and(X1, mark(X2)) -> and(X1, X2)
                       , and(active(X1), X2) -> and(X1, X2)
                       , and(X1, active(X2)) -> and(X1, X2)
                       , isNePal(mark(X)) -> isNePal(X)
                       , isNePal(active(X)) -> isNePal(X)}
                    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:
                    {  active_0(2) -> 1
                     , ___0(2, 2) -> 1
                     , mark_0(2) -> 1
                     , nil_0() -> 2
                     , and_0(2, 2) -> 1
                     , tt_0() -> 2
                     , isNePal_0(2) -> 1}

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