YES

Problem:
 strict:
  l(m(x)) -> m(l(x))
  m(r(x)) -> r(m(x))
  f(m(x),y) -> f(x,m(y))
 weak:
  b() -> l(b())
  f(x,y) -> f(x,r(y))

Proof:
 Matrix Interpretation Processor: dim=5
  
  interpretation:
         [0]
         [0]
   [b] = [0]
         [1]
         [0],
   
             [1 0 0 0 0]     [0]
             [0 1 0 0 0]     [0]
   [l](x0) = [1 0 0 0 0]x0 + [0]
             [1 0 0 0 0]     [1]
             [1 1 0 0 0]     [0],
   
                 [1 1 0 0 0]     [1 0 0 0 0]     [0]
                 [1 1 0 0 0]     [0 0 0 1 0]     [0]
   [f](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 1]x1 + [0]
                 [0 0 0 0 0]     [0 0 0 0 1]     [1]
                 [1 1 0 0 0]     [0 0 0 0 0]     [0],
   
             [1 0 0 0 0]     [1]
             [0 1 0 0 0]     [1]
   [m](x0) = [1 0 0 0 0]x0 + [0]
             [0 0 0 0 0]     [0]
             [0 0 0 0 0]     [0],
   
             [1 0 0 0 0]  
             [1 0 0 0 0]  
   [r](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]    [1]          
             [0 1 0 0 0]    [1]    [0 1 0 0 0]    [1]          
   l(m(x)) = [1 0 0 0 0]x + [1] >= [1 0 0 0 0]x + [0] = m(l(x))
             [1 0 0 0 0]    [2]    [0 0 0 0 0]    [0]          
             [1 1 0 0 0]    [2]    [0 0 0 0 0]    [0]          
   
             [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]          
             [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]          
   m(r(x)) = [1 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = r(m(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 1 0 0 0]    [1 0 0 0 0]    [2]    [1 1 0 0 0]    [1 0 0 0 0]    [1]            
               [1 1 0 0 0]    [0 0 0 1 0]    [2]    [1 1 0 0 0]    [0 0 0 0 0]    [0]            
   f(m(x),y) = [0 0 0 0 0]x + [0 0 0 0 1]y + [0] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0] = f(x,m(y))
               [0 0 0 0 0]    [0 0 0 0 1]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [1]            
               [1 1 0 0 0]    [0 0 0 0 0]    [2]    [1 1 0 0 0]    [0 0 0 0 0]    [0]            
   
         [0]    [0]         
         [0]    [0]         
   b() = [0] >= [0] = l(b())
         [1]    [1]         
         [0]    [0]         
   
            [1 1 0 0 0]    [1 0 0 0 0]    [0]    [1 1 0 0 0]    [1 0 0 0 0]    [0]            
            [1 1 0 0 0]    [0 0 0 1 0]    [0]    [1 1 0 0 0]    [0 0 0 0 0]    [0]            
   f(x,y) = [0 0 0 0 0]x + [0 0 0 0 1]y + [0] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0] = f(x,r(y))
            [0 0 0 0 0]    [0 0 0 0 1]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [1]            
            [1 1 0 0 0]    [0 0 0 0 0]    [0]    [1 1 0 0 0]    [0 0 0 0 0]    [0]            
  problem:
   strict:
    l(m(x)) -> m(l(x))
    m(r(x)) -> r(m(x))
   weak:
    b() -> l(b())
    f(x,y) -> f(x,r(y))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
          [0]
    [b] = [1],
    
              [1 0]  
    [l](x0) = [0 0]x0,
    
                  [2 0]     [1 0]  
    [f](x0, x1) = [0 0]x0 + [0 0]x1,
    
              [2 2]  
    [m](x0) = [0 1]x0,
    
                   [0]
    [r](x0) = x0 + [1]
   orientation:
              [2 2]     [2 0]           
    l(m(x)) = [0 0]x >= [0 0]x = m(l(x))
    
              [2 2]    [2]    [2 2]    [0]          
    m(r(x)) = [0 1]x + [1] >= [0 1]x + [1] = r(m(x))
    
          [0]    [0]         
    b() = [1] >= [0] = l(b())
    
             [2 0]    [1 0]     [2 0]    [1 0]             
    f(x,y) = [0 0]x + [0 0]y >= [0 0]x + [0 0]y = f(x,r(y))
   problem:
    strict:
     l(m(x)) -> m(l(x))
    weak:
     b() -> l(b())
     f(x,y) -> f(x,r(y))
   Matrix Interpretation Processor: dim=5
    
    interpretation:
           [0]
           [0]
     [b] = [0]
           [0]
           [0],
     
               [1 0 1 0 0]  
               [0 0 0 0 0]  
     [l](x0) = [1 0 0 0 0]x0
               [0 0 0 0 0]  
               [0 0 0 0 0]  ,
     
                   [1 0 0 0 0]     [1 1 1 0 0]     [1]
                   [0 0 0 0 0]     [0 0 1 1 1]     [0]
     [f](x0, x1) = [0 0 0 0 0]x0 + [1 0 1 1 1]x1 + [0]
                   [0 0 0 0 0]     [1 0 1 1 0]     [1]
                   [0 0 0 0 0]     [0 1 1 0 0]     [1],
     
               [1 0 1 0 0]     [1]
               [0 0 0 0 0]     [0]
     [m](x0) = [1 0 0 0 0]x0 + [1]
               [0 0 0 0 0]     [0]
               [0 0 0 0 0]     [0],
     
               [1 0 0 0 0]  
               [0 1 1 0 0]  
     [r](x0) = [0 0 0 0 0]x0
               [0 0 1 0 0]  
               [0 0 0 1 1]  
    orientation:
               [2 0 1 0 0]    [2]    [2 0 1 0 0]    [1]          
               [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]          
     l(m(x)) = [1 0 1 0 0]x + [1] >= [1 0 1 0 0]x + [1] = m(l(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]          
     
           [0]    [0]         
           [0]    [0]         
     b() = [0] >= [0] = l(b())
           [0]    [0]         
           [0]    [0]         
     
              [1 0 0 0 0]    [1 1 1 0 0]    [1]    [1 0 0 0 0]    [1 1 1 0 0]    [1]            
              [0 0 0 0 0]    [0 0 1 1 1]    [0]    [0 0 0 0 0]    [0 0 1 1 1]    [0]            
     f(x,y) = [0 0 0 0 0]x + [1 0 1 1 1]y + [0] >= [0 0 0 0 0]x + [1 0 1 1 1]y + [0] = f(x,r(y))
              [0 0 0 0 0]    [1 0 1 1 0]    [1]    [0 0 0 0 0]    [1 0 1 0 0]    [1]            
              [0 0 0 0 0]    [0 1 1 0 0]    [1]    [0 0 0 0 0]    [0 1 1 0 0]    [1]            
    problem:
     strict:
      
     weak:
      b() -> l(b())
      f(x,y) -> f(x,r(y))
    Qed