We consider the following Problem:

  Strict Trs:
    {p(a(x0), p(b(x1), p(a(x2), x3))) ->
     p(x2, p(a(a(x0)), p(b(x1), x3)))}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {p(a(x0), p(b(x1), p(a(x2), x3))) ->
       p(x2, p(a(a(x0)), p(b(x1), x3)))}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs:
        {p(a(x0), p(b(x1), p(a(x2), x3))) ->
         p(x2, p(a(a(x0)), p(b(x1), x3)))}
      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:
      {  p_0(2, 2) -> 1
       , a_0(2) -> 2
       , b_0(2) -> 2}

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