We consider the following Problem:

  Strict Trs: {f(x, f(a(), a())) -> f(f(x, a()), x)}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs: {f(x, f(a(), a())) -> f(f(x, a()), x)}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs: {f(x, f(a(), a())) -> f(f(x, a()), x)}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^2))
    
    Proof:
      The following argument positions are usable:
        Uargs(f) = {}
      We have the following constructor-based EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
      Interpretation Functions:
       f(x1, x2) = [0 2 2] x1 + [0 0 1] x2 + [0]
                   [0 0 0]      [0 0 0]      [0]
                   [0 1 0]      [0 0 0]      [0]
       a() = [0]
             [2]
             [0]

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