We consider the following Problem:

  Strict Trs:
    {  and(x, or(y, z)) -> or(and(x, y), and(x, z))
     , and(x, and(y, y)) -> and(x, y)
     , or(or(x, y), and(y, z)) -> or(x, y)
     , or(x, and(x, y)) -> x
     , or(true(), y) -> true()
     , or(x, false()) -> x
     , or(x, x) -> x
     , or(x, or(y, y)) -> or(x, y)
     , and(x, true()) -> x
     , and(false(), y) -> false()
     , and(x, x) -> x}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  Arguments of following rules are not normal-forms:
  {  and(x, and(y, y)) -> and(x, y)
   , or(x, or(y, y)) -> or(x, y)}
  
  All above mentioned rules can be savely removed.
  
  We consider the following Problem:
  
    Strict Trs:
      {  and(x, or(y, z)) -> or(and(x, y), and(x, z))
       , or(or(x, y), and(y, z)) -> or(x, y)
       , or(x, and(x, y)) -> x
       , or(true(), y) -> true()
       , or(x, false()) -> x
       , or(x, x) -> x
       , and(x, true()) -> x
       , and(false(), y) -> false()
       , and(x, x) -> x}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs:
        {  and(x, or(y, z)) -> or(and(x, y), and(x, z))
         , or(or(x, y), and(y, z)) -> or(x, y)
         , or(x, and(x, y)) -> x
         , or(true(), y) -> true()
         , or(x, false()) -> x
         , or(x, x) -> x
         , and(x, true()) -> x
         , and(false(), y) -> false()
         , and(x, x) -> x}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^2))
    
    Proof:
      The following argument positions are usable:
        Uargs(and) = {}, Uargs(or) = {1, 2}
      We have the following restricted  polynomial interpretation:
      Interpretation Functions:
       [and](x1, x2) = 3 + 2*x1 + 3*x1*x2 + 3*x2^2
       [or](x1, x2) = 2 + x1 + 3*x2
       [true]() = 0
       [false]() = 0

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