YES

Problem:
 f(a,empty()) -> g(a,empty())
 f(a,cons(x,k)) -> f(cons(x,a),k)
 g(empty(),d) -> d
 g(cons(x,k),d) -> g(k,cons(x,d))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 0 0]     [1 1 0]     [0]
   [f](x0, x1) = [1 0 0]x0 + [1 0 1]x1 + [0]
                 [0 0 0]     [0 0 0]     [1],
   
                    [1 0 0]          [1]
   [cons](x0, x1) = [0 0 0]x0 + x1 + [0]
                    [0 0 0]          [0],
   
             [0]
   [empty] = [1]
             [1],
   
                 [1 0 0]       
   [g](x0, x1) = [0 0 0]x0 + x1
                 [0 0 0]       
  orientation:
                  [1 0 0]    [1]    [1 0 0]    [0]               
   f(a,empty()) = [1 0 0]a + [1] >= [0 0 0]a + [1] = g(a,empty())
                  [0 0 0]    [1]    [0 0 0]    [1]               
   
                    [1 0 0]    [1 1 0]    [1 0 0]    [1]    [1 0 0]    [1 1 0]    [1 0 0]    [1]                 
   f(a,cons(x,k)) = [1 0 0]a + [1 0 1]k + [1 0 0]x + [1] >= [1 0 0]a + [1 0 1]k + [1 0 0]x + [1] = f(cons(x,a),k)
                    [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                 
   
                            
   g(empty(),d) = d >= d = d
                            
   
                        [1 0 0]    [1 0 0]    [1]        [1 0 0]    [1 0 0]    [1]                 
   g(cons(x,k),d) = d + [0 0 0]k + [0 0 0]x + [0] >= d + [0 0 0]k + [0 0 0]x + [0] = g(k,cons(x,d))
                        [0 0 0]    [0 0 0]    [0]        [0 0 0]    [0 0 0]    [0]                 
  problem:
   f(a,cons(x,k)) -> f(cons(x,a),k)
   g(empty(),d) -> d
   g(cons(x,k),d) -> g(k,cons(x,d))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1) = 2x0 + 2x1,
    
    [cons](x0, x1) = 4x0 + x1,
    
    [empty] = 1,
    
    [g](x0, x1) = 6x0 + 4x1 + 3
   orientation:
    f(a,cons(x,k)) = 2a + 2k + 8x >= 2a + 2k + 8x = f(cons(x,a),k)
    
    g(empty(),d) = 4d + 9 >= d = d
    
    g(cons(x,k),d) = 4d + 6k + 24x + 3 >= 4d + 6k + 16x + 3 = g(k,cons(x,d))
   problem:
    f(a,cons(x,k)) -> f(cons(x,a),k)
    g(cons(x,k),d) -> g(k,cons(x,d))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [f](x0, x1) = x0 + x1,
     
     [cons](x0, x1) = x0 + x1 + 1,
     
     [g](x0, x1) = 3x0 + 2x1 + 6
    orientation:
     f(a,cons(x,k)) = a + k + x + 1 >= a + k + x + 1 = f(cons(x,a),k)
     
     g(cons(x,k),d) = 2d + 3k + 3x + 9 >= 2d + 3k + 2x + 8 = g(k,cons(x,d))
    problem:
     f(a,cons(x,k)) -> f(cons(x,a),k)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 0 0]     [1 0 1]  
      [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
      
                       [1 0 0]     [1 0 0]     [0]
      [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                       [0 0 0]     [0 0 1]     [1]
     orientation:
                       [1 0 0]    [1 0 1]    [1 0 0]    [1]    [1 0 0]    [1 0 1]    [1 0 0]                  
      f(a,cons(x,k)) = [0 0 0]a + [0 0 0]k + [0 0 0]x + [0] >= [0 0 0]a + [0 0 0]k + [0 0 0]x = f(cons(x,a),k)
                       [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                  
     problem:
      
     Qed