We consider the following Problem:

  Strict Trs:
    {p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2))}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2))}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs:
        {p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2))}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      The following argument positions are usable:
        Uargs(p) = {2}, Uargs(a) = {}, Uargs(b) = {}
      We have the following constructor-based EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       p(x1, x2) = [0 0] x1 + [1 1] x2 + [0]
                   [2 2]      [0 1]      [0]
       a(x1) = [0 2] x1 + [0]
               [0 0]      [0]
       b(x1) = [0 0] x1 + [0]
               [0 0]      [2]

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