YES

Problem:
 strict:
  s(a(x)) -> s(b(x))
  b(b(x)) -> a(x)
 weak:
  f(s(x),y) -> f(x,s(y))
  s(a(x)) -> a(s(x))
  s(b(x)) -> b(s(x))
  a(s(x)) -> s(a(x))
  b(s(x)) -> s(b(x))

Proof:
 Matrix Interpretation Processor: dim=5
  
  interpretation:
             [1 0 0 0 0]  
             [0 0 0 0 1]  
   [s](x0) = [0 0 0 0 0]x0
             [0 1 1 0 0]  
             [0 0 0 1 0]  ,
   
                 [1 1 0 1 1]     [1 0 1 0 0]  
                 [0 0 0 0 0]     [0 1 1 1 1]  
   [f](x0, x1) = [0 0 0 0 0]x0 + [0 0 1 0 0]x1
                 [0 1 0 1 1]     [0 0 1 0 0]  
                 [0 0 0 0 0]     [0 0 1 0 0]  ,
   
             [1 1 1 1 1]     [0]
             [0 1 0 1 1]     [1]
   [a](x0) = [0 0 1 0 0]x0 + [0]
             [0 1 1 1 1]     [1]
             [0 1 1 1 1]     [1],
   
             [1 1 1 1 1]     [0]
             [0 1 0 0 1]     [1]
   [b](x0) = [0 0 1 0 0]x0 + [0]
             [0 1 1 1 0]     [1]
             [0 0 0 1 1]     [1]
  orientation:
             [1 1 1 1 1]    [0]    [1 1 1 1 1]    [0]          
             [0 1 1 1 1]    [1]    [0 0 0 1 1]    [1]          
   s(a(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(b(x))
             [0 1 1 1 1]    [1]    [0 1 1 0 1]    [1]          
             [0 1 1 1 1]    [1]    [0 1 1 1 0]    [1]          
   
             [1 3 3 3 3]    [3]    [1 1 1 1 1]    [0]       
             [0 1 0 1 2]    [3]    [0 1 0 1 1]    [1]       
   b(b(x)) = [0 0 1 0 0]x + [0] >= [0 0 1 0 0]x + [0] = a(x)
             [0 2 2 1 1]    [3]    [0 1 1 1 1]    [1]       
             [0 1 1 2 1]    [3]    [0 1 1 1 1]    [1]       
   
               [1 1 1 1 1]    [1 0 1 0 0]     [1 1 0 1 1]    [1 0 0 0 0]             
               [0 0 0 0 0]    [0 1 1 1 1]     [0 0 0 0 0]    [0 1 1 1 1]             
   f(s(x),y) = [0 0 0 0 0]x + [0 0 1 0 0]y >= [0 0 0 0 0]x + [0 0 0 0 0]y = f(x,s(y))
               [0 1 1 1 1]    [0 0 1 0 0]     [0 1 0 1 1]    [0 0 0 0 0]             
               [0 0 0 0 0]    [0 0 1 0 0]     [0 0 0 0 0]    [0 0 0 0 0]             
   
             [1 1 1 1 1]    [0]    [1 1 1 1 1]    [0]          
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
   s(a(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = a(s(x))
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
   
             [1 1 1 1 1]    [0]    [1 1 1 1 1]    [0]          
             [0 0 0 1 1]    [1]    [0 0 0 1 1]    [1]          
   s(b(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = b(s(x))
             [0 1 1 0 1]    [1]    [0 1 1 0 1]    [1]          
             [0 1 1 1 0]    [1]    [0 1 1 1 0]    [1]          
   
             [1 1 1 1 1]    [0]    [1 1 1 1 1]    [0]          
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
   a(s(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(a(x))
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
             [0 1 1 1 1]    [1]    [0 1 1 1 1]    [1]          
   
             [1 1 1 1 1]    [0]    [1 1 1 1 1]    [0]          
             [0 0 0 1 1]    [1]    [0 0 0 1 1]    [1]          
   b(s(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(b(x))
             [0 1 1 0 1]    [1]    [0 1 1 0 1]    [1]          
             [0 1 1 1 0]    [1]    [0 1 1 1 0]    [1]          
  problem:
   strict:
    s(a(x)) -> s(b(x))
   weak:
    f(s(x),y) -> f(x,s(y))
    s(a(x)) -> a(s(x))
    s(b(x)) -> b(s(x))
    a(s(x)) -> s(a(x))
    b(s(x)) -> s(b(x))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
              [1 0 0 0 0]     [0]
              [0 0 0 0 0]     [0]
    [s](x0) = [0 0 1 0 0]x0 + [0]
              [0 1 0 0 0]     [1]
              [0 1 0 1 1]     [0],
    
                  [1 0 0 1 1]     [1 0 0 0 0]     [0]
                  [0 0 0 0 0]     [0 0 0 0 0]     [1]
    [f](x0, x1) = [0 0 0 1 1]x0 + [0 1 1 0 0]x1 + [1]
                  [0 0 0 0 0]     [0 0 0 0 0]     [0]
                  [0 0 0 0 1]     [0 1 0 0 0]     [0],
    
              [1 0 0 0 0]     [0]
              [0 0 0 0 0]     [0]
    [a](x0) = [0 0 0 0 0]x0 + [0]
              [0 1 0 0 0]     [1]
              [1 1 0 1 1]     [0],
    
              [1 0 0 0 0]     [0]
              [0 0 0 0 0]     [0]
    [b](x0) = [0 0 0 0 0]x0 + [0]
              [0 1 0 0 0]     [1]
              [1 1 0 1 1]     [0]
   orientation:
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    s(a(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(b(x))
              [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]          
              [1 2 0 1 1]    [1]    [1 2 0 1 1]    [1]          
    
                [1 2 0 1 1]    [1 0 0 0 0]    [1]    [1 0 0 1 1]    [1 0 0 0 0]    [0]            
                [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [1]            
    f(s(x),y) = [0 2 0 1 1]x + [0 1 1 0 0]y + [2] >= [0 0 0 1 1]x + [0 0 1 0 0]y + [1] = f(x,s(y))
                [0 0 0 0 0]    [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0 0 0 0 0]    [0]            
                [0 1 0 1 1]    [0 1 0 0 0]    [0]    [0 0 0 0 1]    [0 0 0 0 0]    [0]            
    
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    s(a(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = a(s(x))
              [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]          
              [1 2 0 1 1]    [1]    [1 2 0 1 1]    [1]          
    
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    s(b(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = b(s(x))
              [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]          
              [1 2 0 1 1]    [1]    [1 2 0 1 1]    [1]          
    
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    a(s(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(a(x))
              [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]          
              [1 2 0 1 1]    [1]    [1 2 0 1 1]    [1]          
    
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    b(s(x)) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = s(b(x))
              [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]          
              [1 2 0 1 1]    [1]    [1 2 0 1 1]    [1]          
   problem:
    strict:
     s(a(x)) -> s(b(x))
    weak:
     s(a(x)) -> a(s(x))
     s(b(x)) -> b(s(x))
     a(s(x)) -> s(a(x))
     b(s(x)) -> s(b(x))
   String Reversal Processor:
    strict:
     a(s(x)) -> b(s(x))
    weak:
     a(s(x)) -> s(a(x))
     b(s(x)) -> s(b(x))
     s(a(x)) -> a(s(x))
     s(b(x)) -> b(s(x))
    Arctic Interpretation Processor:
     dimension: 3
     interpretation:
                [0  0  0 ]  
      [s](x0) = [0  0  0 ]x0
                [-& 0  -&]  ,
      
                [1  0  -&]  
      [a](x0) = [1  1  1 ]x0
                [1  0  -&]  ,
      
                [0 0 0]  
      [b](x0) = [0 0 0]x0
                [0 0 0]  
     orientation:
                [1 1 1]     [0 0 0]           
      a(s(x)) = [1 1 1]x >= [0 0 0]x = b(s(x))
                [1 1 1]     [0 0 0]           
      
                [1 1 1]     [1 1 1]           
      a(s(x)) = [1 1 1]x >= [1 1 1]x = s(a(x))
                [1 1 1]     [1 1 1]           
      
                [0 0 0]     [0 0 0]           
      b(s(x)) = [0 0 0]x >= [0 0 0]x = s(b(x))
                [0 0 0]     [0 0 0]           
      
                [1 1 1]     [1 1 1]           
      s(a(x)) = [1 1 1]x >= [1 1 1]x = a(s(x))
                [1 1 1]     [1 1 1]           
      
                [0 0 0]     [0 0 0]           
      s(b(x)) = [0 0 0]x >= [0 0 0]x = b(s(x))
                [0 0 0]     [0 0 0]           
     problem:
      strict:
       
      weak:
       a(s(x)) -> s(a(x))
       b(s(x)) -> s(b(x))
       s(a(x)) -> a(s(x))
       s(b(x)) -> b(s(x))
     Qed