Problem:
 average(s(x),y) -> average(x,s(y))
 average(x,s(s(s(y)))) -> s(average(s(x),y))
 average(0(),0()) -> 0()
 average(0(),s(0())) -> 0()
 average(0(),s(s(0()))) -> s(0())

Proof:
 Complexity Transformation Processor:
  strict:
   average(s(x),y) -> average(x,s(y))
   average(x,s(s(s(y)))) -> s(average(s(x),y))
   average(0(),0()) -> 0()
   average(0(),s(0())) -> 0()
   average(0(),s(s(0()))) -> s(0())
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [0] = 128,
     
     [average](x0, x1) = x0 + x1 + 16,
     
     [s](x0) = x0 + 3
    orientation:
     average(s(x),y) = x + y + 19 >= x + y + 19 = average(x,s(y))
     
     average(x,s(s(s(y)))) = x + y + 25 >= x + y + 22 = s(average(s(x),y))
     
     average(0(),0()) = 272 >= 128 = 0()
     
     average(0(),s(0())) = 275 >= 128 = 0()
     
     average(0(),s(s(0()))) = 278 >= 131 = s(0())
    problem:
     strict:
      average(s(x),y) -> average(x,s(y))
     weak:
      average(x,s(s(s(y)))) -> s(average(s(x),y))
      average(0(),0()) -> 0()
      average(0(),s(0())) -> 0()
      average(0(),s(s(0()))) -> s(0())
    Matrix Interpretation Processor:
     dimension: 3
     max_matrix:
      [1 0 1]
      [0 0 0]
      [0 0 1]
      interpretation:
             [0]
       [0] = [0]
             [0],
       
                           [1 0 1]     [1 0 0]  
       [average](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                           [0 0 1]     [0 0 1]  ,
       
                 [1 0 0]     [1]
       [s](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [1]
      orientation:
                         [1 0 1]    [1 0 0]    [2]    [1 0 1]    [1 0 0]    [1]                  
       average(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = average(x,s(y))
                         [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]                  
       
                               [1 0 1]    [1 0 0]    [3]    [1 0 1]    [1 0 0]    [3]                     
       average(x,s(s(s(y)))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = s(average(s(x),y))
                               [0 0 1]    [0 0 1]    [3]    [0 0 1]    [0 0 1]    [2]                     
       
                          [0]    [0]      
       average(0(),0()) = [0] >= [0] = 0()
                          [0]    [0]      
       
                             [1]    [0]      
       average(0(),s(0())) = [0] >= [0] = 0()
                             [1]    [0]      
       
                                [2]    [1]         
       average(0(),s(s(0()))) = [0] >= [0] = s(0())
                                [2]    [1]         
      problem:
       strict:
        
       weak:
        average(s(x),y) -> average(x,s(y))
        average(x,s(s(s(y)))) -> s(average(s(x),y))
        average(0(),0()) -> 0()
        average(0(),s(0())) -> 0()
        average(0(),s(s(0()))) -> s(0())
      Qed