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:
 Bounds Processor:
  bound: 1
  enrichment: match-rt
  automaton:
   final states: {6}
   transitions:
    m0(6) -> 6*
    f0(6,6) -> 6*
    r0(6) -> 6*
    f1(6,20) -> 6*
    r1(20) -> 20*
    r1(6) -> 20*
    l0(6) -> 6*
    b0() -> 6*
    l1(39) -> 39,6
    m1(20) -> 20*
    m1(6) -> 20*
    b1() -> 39*
  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=2
    
    interpretation:
           [0]
     [b] = [0],
     
               [2 2]  
     [l](x0) = [0 2]x0,
     
                   [2 0]     [2 0]     [2]
     [f](x0, x1) = [0 0]x0 + [0 1]x1 + [0],
     
                    [0]
     [m](x0) = x0 + [1],
     
                 
     [r](x0) = x0
    orientation:
               [2 2]    [2]    [2 2]    [0]          
     l(m(x)) = [0 2]x + [2] >= [0 2]x + [1] = m(l(x))
     
           [0]    [0]         
     b() = [0] >= [0] = l(b())
     
              [2 0]    [2 0]    [2]    [2 0]    [2 0]    [2]            
     f(x,y) = [0 0]x + [0 1]y + [0] >= [0 0]x + [0 1]y + [0] = f(x,r(y))
    problem:
     strict:
      
     weak:
      b() -> l(b())
      f(x,y) -> f(x,r(y))
    Qed