We consider the following Problem:

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

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

Proof:
  We consider the following Problem:
  
    Strict Trs: {a(b(x)) -> b(b(a(x)))}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    We consider the following Problem:
    
      Strict Trs: {a(b(x)) -> b(b(a(x)))}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with the following automaton:
      {  a_0(2) -> 1
       , a_1(2) -> 4
       , b_0(2) -> 2
       , b_1(3) -> 1
       , b_1(3) -> 4
       , b_1(4) -> 3}

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