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=2
  
  interpretation:
               
   [s](x0) = x0,
   
                 [2 2]     [1 2]     [0]
   [f](x0, x1) = [0 0]x0 + [2 0]x1 + [2],
   
             [1 0]     [1]
   [a](x0) = [0 0]x0 + [0],
   
             [1 0]     [1]
   [b](x0) = [0 0]x0 + [0]
  orientation:
             [1 0]    [1]    [1 0]    [1]          
   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
   
             [1 0]    [2]    [1 0]    [1]       
   b(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(x)
   
               [2 2]    [1 2]    [0]    [2 2]    [1 2]    [0]            
   f(s(x),y) = [0 0]x + [2 0]y + [2] >= [0 0]x + [2 0]y + [2] = f(x,s(y))
   
             [1 0]    [1]    [1 0]    [1]          
   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(s(x))
   
             [1 0]    [1]    [1 0]    [1]          
   s(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = b(s(x))
   
             [1 0]    [1]    [1 0]    [1]          
   a(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(a(x))
   
             [1 0]    [1]    [1 0]    [1]          
   b(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
  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]  
    [s](x0) = [0 0 1 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  ,
    
                  [1 0 0 0 0]     [1 1 0 1 0]     [1]
                  [0 0 0 0 0]     [0 0 1 0 0]     [0]
    [f](x0, x1) = [0 0 1 0 0]x0 + [0 0 0 0 1]x1 + [0]
                  [0 0 0 0 0]     [0 0 0 0 0]     [0]
                  [0 0 0 0 0]     [0 0 1 1 0]     [0],
    
              [1 0 0 0 0]     [1]
              [0 0 0 0 0]     [0]
    [a](x0) = [0 0 0 0 0]x0 + [0]
              [0 0 0 0 0]     [0]
              [0 0 0 0 0]     [0],
    
              [1 0 0 0 0]  
              [0 0 0 0 0]  
    [b](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  
   orientation:
              [1 0 0 0 0]    [1]    [1 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 = s(b(x))
              [0 0 0 0 0]    [0]    [0 0 0 0 0]           
              [0 0 0 0 0]    [0]    [0 0 0 0 0]           
    
                [1 0 0 0 0]    [1 1 0 1 0]    [1]    [1 0 0 0 0]    [1 0 0 0 0]    [1]            
                [0 0 0 0 0]    [0 0 1 0 0]    [0]    [0 0 0 0 0]    [0 0 1 0 0]    [0]            
    f(s(x),y) = [0 0 1 0 0]x + [0 0 0 0 1]y + [0] >= [0 0 1 0 0]x + [0 0 0 0 0]y + [0] = 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 0 0 0 0]    [0 0 1 1 0]    [0]    [0 0 0 0 0]    [0 0 1 0 0]    [0]            
    
              [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]          
              [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]    [0]    [0 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    
              [1 0 0 0 0]     [1 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]x = b(s(x))
              [0 0 0 0 0]     [0 0 0 0 0]           
              [0 0 0 0 0]     [0 0 0 0 0]           
    
              [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]          
              [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]    [0]    [0 0 0 0 0]    [0]          
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
    
              [1 0 0 0 0]     [1 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]x = s(b(x))
              [0 0 0 0 0]     [0 0 0 0 0]           
              [0 0 0 0 0]     [0 0 0 0 0]           
   problem:
    strict:
     
    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))
   Qed