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 1]          [0]
   [cons](x0, x1) = [0 0 1]x0 + x1 + [0]
                    [0 0 0]          [1],
   
                 [1 0 0]     [1 0 0]  
   [g](x0, x1) = [0 1 1]x0 + [0 1 0]x1
                 [0 1 1]     [0 1 1]  ,
   
                 [1 0 0]     [1 0 1]  
   [f](x0, x1) = [0 1 1]x0 + [0 1 1]x1
                 [0 1 1]     [1 0 1]  ,
   
             [0]
   [empty] = [0]
             [1]
  orientation:
                  [1 0 0]    [1]    [1 0 0]    [0]               
   f(a,empty()) = [0 1 1]a + [1] >= [0 1 1]a + [0] = g(a,empty())
                  [0 1 1]    [1]    [0 1 1]    [1]               
   
                    [1 0 0]    [1 0 1]    [1 0 1]    [1]    [1 0 0]    [1 0 1]    [1 0 1]    [0]                 
   f(a,cons(x,k)) = [0 1 1]a + [0 1 1]k + [0 0 1]x + [1] >= [0 1 1]a + [0 1 1]k + [0 0 1]x + [1] = f(cons(x,a),k)
                    [0 1 1]    [1 0 1]    [1 0 1]    [1]    [0 1 1]    [1 0 1]    [0 0 1]    [1]                 
   
                  [1 0 0]    [0]         
   g(empty(),d) = [0 1 0]d + [1] >= d = d
                  [0 1 1]    [1]         
   
                    [1 0 0]    [1 0 0]    [1 0 1]    [0]    [1 0 0]    [1 0 0]    [1 0 1]    [0]                 
   g(cons(x,k),d) = [0 1 0]d + [0 1 1]k + [0 0 1]x + [1] >= [0 1 0]d + [0 1 1]k + [0 0 1]x + [0] = g(k,cons(x,d))
                    [0 1 1]    [0 1 1]    [0 0 1]    [1]    [0 1 1]    [0 1 1]    [0 0 1]    [1]                 
  problem:
   g(empty(),d) -> d
   g(cons(x,k),d) -> g(k,cons(x,d))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]          [0]
    [cons](x0, x1) = [0 0 0]x0 + x1 + [0]
                     [0 0 0]          [1],
    
                  [1 0 1]     [1 0 0]  
    [g](x0, x1) = [0 0 1]x0 + [0 1 1]x1
                  [0 0 1]     [0 0 1]  ,
    
              [1]
    [empty] = [0]
              [0]
   orientation:
                   [1 0 0]    [1]         
    g(empty(),d) = [0 1 1]d + [0] >= d = d
                   [0 0 1]    [0]         
    
                     [1 0 0]    [1 0 1]    [1 0 0]    [1]    [1 0 0]    [1 0 1]    [1 0 0]    [0]                 
    g(cons(x,k),d) = [0 1 1]d + [0 0 1]k + [0 0 0]x + [1] >= [0 1 1]d + [0 0 1]k + [0 0 0]x + [1] = g(k,cons(x,d))
                     [0 0 1]    [0 0 1]    [0 0 0]    [1]    [0 0 1]    [0 0 1]    [0 0 0]    [1]                 
   problem:
    
   Qed