YES

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

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]     [0]
   [g](x0) = [2 1]x0 + [1],
   
         [0]
   [b] = [1],
   
         [0]
   [a] = [1],
   
                     [2 1]     [1 1]     [2 0]     [0]
   [f](x0, x1, x2) = [0 2]x0 + [0 0]x1 + [0 0]x2 + [1]
  orientation:
                   [3 1]    [2 0]    [2]    [3 1]    [1]                
   f(a(),g(y),z) = [0 0]y + [0 0]z + [3] >= [0 0]y + [3] = f(a(),y,g(y))
   
                   [3 1]    [2 0]    [2]    [1 1]    [2 0]    [1]             
   f(b(),g(y),z) = [0 0]y + [0 0]z + [3] >= [0 0]y + [0 0]z + [3] = f(a(),y,z)
   
         [0]    [0]      
   a() = [1] >= [1] = b()
   
              [2 1]    [1 1]    [2 0]    [0]    [2 1]    [1 1]    [2 0]    [0]              
   f(x,y,z) = [0 2]x + [0 0]y + [0 0]z + [1] >= [0 2]x + [0 0]y + [0 0]z + [1] = f(x,y,g(z))
  problem:
   strict:
    a() -> b()
   weak:
    f(x,y,z) -> f(x,y,g(z))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
              [1 0 0 0 0]  
              [0 0 0 0 0]  
    [g](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  ,
    
          [0]
          [0]
    [b] = [0]
          [0]
          [0],
    
          [1]
          [0]
    [a] = [0]
          [0]
          [0],
    
                      [1 0 0 0 0]     [1 0 0 0 0]     [1 0 0 0 0]     [0]
                      [0 0 0 0 0]     [0 0 0 0 0]     [0 0 0 0 0]     [0]
    [f](x0, x1, x2) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1 + [0 1 0 0 0]x2 + [1]
                      [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 0 0]     [0]
   orientation:
          [1]    [0]      
          [0]    [0]      
    a() = [0] >= [0] = b()
          [0]    [0]      
          [0]    [0]      
    
               [1 0 0 0 0]    [1 0 0 0 0]    [1 0 0 0 0]    [0]    [1 0 0 0 0]    [1 0 0 0 0]    [1 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 0 0]    [0 0 0 0 0]    [0]              
    f(x,y,z) = [0 0 0 0 0]x + [0 0 0 0 0]y + [0 1 0 0 0]z + [1] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z + [1] = f(x,y,g(z))
               [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 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]    [0 0 0 0 0]    [0]              
   problem:
    strict:
     
    weak:
     f(x,y,z) -> f(x,y,g(z))
   Qed