We consider the following Problem:

  Strict Trs:
    {  or(x, x) -> x
     , and(x, x) -> x
     , not(not(x)) -> x
     , not(and(x, y)) -> or(not(x), not(y))
     , not(or(x, y)) -> and(not(x), not(y))}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  or(x, x) -> x
       , and(x, x) -> x
       , not(not(x)) -> x
       , not(and(x, y)) -> or(not(x), not(y))
       , not(or(x, y)) -> and(not(x), not(y))}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  or(x, x) -> x
       , not(or(x, y)) -> and(not(x), not(y))}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(or) = {1, 2}, Uargs(and) = {1, 2}, Uargs(not) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       or(x1, x2) = [1 0] x1 + [1 1] x2 + [2]
                    [0 1]      [0 0]      [0]
       and(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
                     [0 1]      [0 0]      [0]
       not(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:
        {  and(x, x) -> x
         , not(not(x)) -> x
         , not(and(x, y)) -> or(not(x), not(y))}
      Weak Trs:
        {  or(x, x) -> x
         , not(or(x, y)) -> and(not(x), not(y))}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      The weightgap principle applies, where following rules are oriented strictly:
      
      TRS Component: {and(x, x) -> x}
      
      Interpretation of nonconstant growth:
      -------------------------------------
        The following argument positions are usable:
          Uargs(or) = {1, 2}, Uargs(and) = {1, 2}, Uargs(not) = {}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         or(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                      [0 0]      [0 1]      [0]
         and(x1, x2) = [1 0] x1 + [1 1] x2 + [1]
                       [0 1]      [0 0]      [0]
         not(x1) = [1 0] x1 + [1]
                   [0 0]      [1]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  not(not(x)) -> x
           , not(and(x, y)) -> or(not(x), not(y))}
        Weak Trs:
          {  and(x, x) -> x
           , or(x, x) -> x
           , not(or(x, y)) -> and(not(x), not(y))}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^1))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component: {not(not(x)) -> x}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(or) = {1, 2}, Uargs(and) = {1, 2}, Uargs(not) = {}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           or(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                        [0 0]      [0 1]      [0]
           and(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                         [0 0]      [0 1]      [0]
           not(x1) = [1 0] x1 + [2]
                     [0 1]      [1]
        
        The strictly oriented rules are moved into the weak component.
        
        We consider the following Problem:
        
          Strict Trs: {not(and(x, y)) -> or(not(x), not(y))}
          Weak Trs:
            {  not(not(x)) -> x
             , and(x, x) -> x
             , or(x, x) -> x
             , not(or(x, y)) -> and(not(x), not(y))}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^1))
        
        Proof:
          We consider the following Problem:
          
            Strict Trs: {not(and(x, y)) -> or(not(x), not(y))}
            Weak Trs:
              {  not(not(x)) -> x
               , and(x, x) -> x
               , or(x, x) -> x
               , not(or(x, y)) -> and(not(x), not(y))}
            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:
            {  or_0(2, 2) -> 1
             , and_0(2, 2) -> 1
             , not_0(2) -> 1}

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