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