YES

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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [0] = 1,
   
   [average](x0, x1) = 3x0 + 3x1 + 1,
   
   [s](x0) = x0
  orientation:
   average(s(x),y) = 3x + 3y + 1 >= 3x + 3y + 1 = average(x,s(y))
   
   average(x,s(s(s(y)))) = 3x + 3y + 1 >= 3x + 3y + 1 = s(average(s(x),y))
   
   average(0(),0()) = 7 >= 1 = 0()
   
   average(0(),s(0())) = 7 >= 1 = 0()
   
   average(0(),s(s(0()))) = 7 >= 1 = s(0())
  problem:
   average(s(x),y) -> average(x,s(y))
   average(x,s(s(s(y)))) -> s(average(s(x),y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [average](x0, x1) = x0 + x1,
    
    [s](x0) = x0 + 5
   orientation:
    average(s(x),y) = x + y + 5 >= x + y + 5 = average(x,s(y))
    
    average(x,s(s(s(y)))) = x + y + 15 >= x + y + 10 = s(average(s(x),y))
   problem:
    average(s(x),y) -> average(x,s(y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                         [1 0 1]     [1 0 0]  
     [average](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                         [0 0 0]     [0 0 0]  ,
     
               [1 0 0]     [0]
     [s](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [1]
    orientation:
                       [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]                   
     average(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = average(x,s(y))
                       [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                   
    problem:
     
    Qed