YES

Problem:
 f(s(X)) -> f(X)
 g(cons(0(),Y)) -> g(Y)
 g(cons(s(X),Y)) -> s(X)
 h(cons(X,Y)) -> h(g(cons(X,Y)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]     [1]
   [h](x0) = [0 0 0]x0 + [0]
             [1 0 0]     [0],
   
             [1 0 0]  
   [g](x0) = [1 0 0]x0
             [0 1 0]  ,
   
                    [1 1 0]     [1 1 0]     [0]
   [cons](x0, x1) = [1 0 0]x0 + [1 1 0]x1 + [1]
                    [0 0 1]     [0 0 0]     [0],
   
         [0]
   [0] = [0]
         [0],
   
             [1 1 0]  
   [f](x0) = [1 0 0]x0
             [0 0 0]  ,
   
             [1 1 0]     [0]
   [s](x0) = [0 0 1]x0 + [1]
             [1 0 0]     [0]
  orientation:
             [1 1 1]    [1]    [1 1 0]        
   f(s(X)) = [1 1 0]X + [0] >= [1 0 0]X = f(X)
             [0 0 0]    [0]    [0 0 0]        
   
                    [1 1 0]    [0]    [1 0 0]        
   g(cons(0(),Y)) = [1 1 0]Y + [0] >= [1 0 0]Y = g(Y)
                    [1 1 0]    [1]    [0 1 0]        
   
                     [1 1 1]    [1 1 0]    [1]    [1 1 0]    [0]       
   g(cons(s(X),Y)) = [1 1 1]X + [1 1 0]Y + [1] >= [0 0 1]X + [1] = s(X)
                     [1 1 0]    [1 1 0]    [1]    [1 0 0]    [0]       
   
                  [1 1 0]    [1 1 0]    [1]    [1 1 0]    [1 1 0]    [1]                  
   h(cons(X,Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y + [0] = h(g(cons(X,Y)))
                  [1 1 0]    [1 1 0]    [0]    [1 1 0]    [1 1 0]    [0]                  
  problem:
   g(cons(0(),Y)) -> g(Y)
   h(cons(X,Y)) -> h(g(cons(X,Y)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]     [0]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 0]  
    [g](x0) = [0 0 0]x0
              [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 0]     [1],
    
          [1]
    [0] = [0]
          [0]
   orientation:
                     [1 0 0]    [1]    [1 0 0]        
    g(cons(0(),Y)) = [0 0 0]Y + [0] >= [0 0 0]Y = g(Y)
                     [0 0 0]    [0]    [0 0 0]        
    
                   [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [0]                  
    h(cons(X,Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y + [0] = h(g(cons(X,Y)))
                   [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                  
   problem:
    
   Qed