We consider the following Problem:

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

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

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  +(-(x, y), z) -> -(+(x, z), y)
       , -(+(x, y), y) -> x}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component: {-(+(x, y), y) -> x}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(+) = {}, Uargs(-) = {1}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       +(x1, x2) = [1 0] x1 + [0 0] x2 + [1]
                   [1 1]      [0 0]      [1]
       -(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                   [0 1]      [0 0]      [0]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs: {+(-(x, y), z) -> -(+(x, z), y)}
      Weak Trs: {-(+(x, y), y) -> x}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      We consider the following Problem:
      
        Strict Trs: {+(-(x, y), z) -> -(+(x, z), y)}
        Weak Trs: {-(+(x, y), y) -> x}
        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:
        {  +_0(2, 2) -> 1
         , -_0(2, 2) -> 1}

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