YES

Problem:
 f(nil()) -> nil()
 f(.(nil(),y)) -> .(nil(),f(y))
 f(.(.(x,y),z)) -> f(.(x,.(y,z)))
 g(nil()) -> nil()
 g(.(x,nil())) -> .(g(x),nil())
 g(.(x,.(y,z))) -> g(.(.(x,y),z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 4x0 + 5,
   
   [.](x0, x1) = x0 + x1,
   
   [f](x0) = 2x0,
   
   [nil] = 0
  orientation:
   f(nil()) = 0 >= 0 = nil()
   
   f(.(nil(),y)) = 2y >= 2y = .(nil(),f(y))
   
   f(.(.(x,y),z)) = 2x + 2y + 2z >= 2x + 2y + 2z = f(.(x,.(y,z)))
   
   g(nil()) = 5 >= 0 = nil()
   
   g(.(x,nil())) = 4x + 5 >= 4x + 5 = .(g(x),nil())
   
   g(.(x,.(y,z))) = 4x + 4y + 4z + 5 >= 4x + 4y + 4z + 5 = g(.(.(x,y),z))
  problem:
   f(nil()) -> nil()
   f(.(nil(),y)) -> .(nil(),f(y))
   f(.(.(x,y),z)) -> f(.(x,.(y,z)))
   g(.(x,nil())) -> .(g(x),nil())
   g(.(x,.(y,z))) -> g(.(.(x,y),z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]  
    [g](x0) = [0 1 0]x0
              [1 0 1]  ,
    
                  [1 0 0]     [1 1 0]     [0]
    [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 1 1]     [0 0 1]     [0],
    
              [1 0 1]  
    [f](x0) = [0 1 0]x0
              [1 0 1]  ,
    
            [0]
    [nil] = [0]
            [1]
   orientation:
               [1]    [0]        
    f(nil()) = [0] >= [0] = nil()
               [1]    [1]        
    
                    [1 1 1]    [1]    [1 1 1]    [0]                
    f(.(nil(),y)) = [0 0 0]y + [1] >= [0 0 0]y + [1] = .(nil(),f(y))
                    [1 1 1]    [1]    [1 0 1]    [1]                
    
                     [1 1 1]    [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [1 1 1]    [1]                 
    f(.(.(x,y),z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] = f(.(x,.(y,z)))
                     [1 1 1]    [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [1 1 1]    [1]                 
    
                    [1 1 1]    [1]    [1 0 1]    [0]                
    g(.(x,nil())) = [0 0 0]x + [1] >= [0 0 0]x + [1] = .(g(x),nil())
                    [1 1 1]    [1]    [1 1 1]    [1]                
    
                     [1 1 1]    [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [1 1 1]    [1]                 
    g(.(x,.(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] = g(.(.(x,y),z))
                     [1 1 1]    [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [1 1 1]    [1]                 
   problem:
    f(.(.(x,y),z)) -> f(.(x,.(y,z)))
    g(.(x,.(y,z))) -> g(.(.(x,y),z))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 1 0]  
     [g](x0) = [0 0 0]x0
               [0 1 0]  ,
     
                   [1 1 1]     [1 0 0]     [0]
     [.](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [0]
                   [0 0 0]     [0 0 0]     [1],
     
               [1 0 0]  
     [f](x0) = [0 0 0]x0
               [0 0 0]  
    orientation:
                      [1 1 1]    [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 1 1]    [1 0 0]                  
     f(.(.(x,y),z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z = f(.(x,.(y,z)))
                      [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                  
     
                      [1 1 1]    [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [1 1 1]    [1]                 
     g(.(x,.(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = g(.(.(x,y),z))
                      [0 0 0]    [0 0 0]    [0 1 1]    [1]    [0 0 0]    [0 0 0]    [0 1 1]    [0]                 
    problem:
     g(.(x,.(y,z))) -> g(.(.(x,y),z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [g](x0) = 2x0 + 1,
      
      [.](x0, x1) = x0 + 2x1 + 4
     orientation:
      g(.(x,.(y,z))) = 2x + 4y + 8z + 25 >= 2x + 4y + 4z + 17 = g(.(.(x,y),z))
     problem:
      
     Qed