We consider the following Problem:

  Strict Trs:
    {  *(x, +(y, z)) -> +(*(x, y), *(x, z))
     , *(+(x, y), z) -> +(*(x, z), *(y, z))
     , *(x, 1()) -> x
     , *(1(), y) -> y}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  *(x, +(y, z)) -> +(*(x, y), *(x, z))
       , *(+(x, y), z) -> +(*(x, z), *(y, z))
       , *(x, 1()) -> x
       , *(1(), y) -> y}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs:
        {  *(x, +(y, z)) -> +(*(x, y), *(x, z))
         , *(+(x, y), z) -> +(*(x, z), *(y, z))
         , *(x, 1()) -> x
         , *(1(), y) -> y}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^2))
    
    Proof:
      The following argument positions are usable:
        Uargs(*) = {}, Uargs(+) = {1, 2}
      We have the following restricted  polynomial interpretation:
      Interpretation Functions:
       [*](x1, x2) = 1 + 3*x1 + 3*x1*x2 + 2*x2
       [+](x1, x2) = 2 + x1 + x2
       [1]() = 3

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