YES

Problem:
 cons_x[1](x2,x1) -> Cons(x2,x1)
 comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) -> cons_x[1](x4,comp_f_g[1](x3,x2,x1))
 comp_f_g[1](cons_x(x3),cons_x(x2),x1) -> cons_x[1](x3,cons_x[1](x2,x1))
 comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) -> comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
 comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) -> comp_f_g[1](x4,x3,cons_x[1](x2,x1))
 rec[walk_0][1](Leaf(x1)) -> cons_x(x1)
 rec[walk_0][1](Node(x2,x1)) -> comp_f_g(rec[walk_0][1](x2),rec[walk_0][1](x1))
 main(Leaf(x2)) -> cons_x[1](x2,Nil())
 main(Node(x4,x2)) -> comp_f_g[1](rec[walk_0][1](x4),rec[walk_0][1](x2),Nil())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [Nil] = 5,
   
   [main](x0) = 5x0 + 6,
   
   [Node](x0, x1) = x0 + 4x1 + 1,
   
   [rec[walk_0][1]](x0) = 4x0,
   
   [Leaf](x0) = x0,
   
   [comp_f_g[1]](x0, x1, x2) = x0 + x1 + x2,
   
   [comp_f_g](x0, x1) = x0 + x1,
   
   [cons_x](x0) = 4x0,
   
   [Cons](x0, x1) = 4x0 + x1,
   
   [cons_x[1]](x0, x1) = 4x0 + x1
  orientation:
   cons_x[1](x2,x1) = x1 + 4x2 >= x1 + 4x2 = Cons(x2,x1)
   
   comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) = x1 + x2 + x3 + 4x4 >= x1 + x2 + x3 + 4x4 = cons_x[1](x4,comp_f_g[1](x3,x2,x1))
   
   comp_f_g[1](cons_x(x3),cons_x(x2),x1) = x1 + 4x2 + 4x3 >= x1 + 4x2 + 4x3 = cons_x[1](x3,cons_x[1](x2,x1))
   
   comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) = x1 + x2 + x3 + x4 + x5 >= x1 + x2 + x3 + x4 + x5 = comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
   
   comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) = x1 + 4x2 + x3 + x4 >= x1 + 4x2 + x3 + x4 = comp_f_g[1](x4,x3,cons_x[1](x2,x1))
   
   rec[walk_0][1](Leaf(x1)) = 4x1 >= 4x1 = cons_x(x1)
   
   rec[walk_0][1](Node(x2,x1)) = 16x1 + 4x2 + 4 >= 4x1 + 4x2 = comp_f_g(rec[walk_0][1](x2),rec[walk_0][1](x1))
   
   main(Leaf(x2)) = 5x2 + 6 >= 4x2 + 5 = cons_x[1](x2,Nil())
   
   main(Node(x4,x2)) = 20x2 + 5x4 + 11 >= 4x2 + 4x4 + 5 = comp_f_g[1](rec[walk_0][1](x4),rec[walk_0][1](x2),Nil())
  problem:
   cons_x[1](x2,x1) -> Cons(x2,x1)
   comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) -> cons_x[1](x4,comp_f_g[1](x3,x2,x1))
   comp_f_g[1](cons_x(x3),cons_x(x2),x1) -> cons_x[1](x3,cons_x[1](x2,x1))
   comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) -> comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
   comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) -> comp_f_g[1](x4,x3,cons_x[1](x2,x1))
   rec[walk_0][1](Leaf(x1)) -> cons_x(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [rec[walk_0][1]](x0) = x0,
    
    [Leaf](x0) = 2x0 + 3,
    
    [comp_f_g[1]](x0, x1, x2) = x0 + x1 + x2,
    
    [comp_f_g](x0, x1) = x0 + x1,
    
    [cons_x](x0) = 2x0,
    
    [Cons](x0, x1) = 2x0 + x1,
    
    [cons_x[1]](x0, x1) = 2x0 + x1
   orientation:
    cons_x[1](x2,x1) = x1 + 2x2 >= x1 + 2x2 = Cons(x2,x1)
    
    comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) = x1 + x2 + x3 + 2x4 >= x1 + x2 + x3 + 2x4 = cons_x[1](x4,comp_f_g[1](x3,x2,x1))
    
    comp_f_g[1](cons_x(x3),cons_x(x2),x1) = x1 + 2x2 + 2x3 >= x1 + 2x2 + 2x3 = cons_x[1](x3,cons_x[1](x2,x1))
    
    comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) = x1 + x2 + x3 + x4 + x5 >= x1 + x2 + x3 + x4 + x5 = comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
    
    comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) = x1 + 2x2 + x3 + x4 >= x1 + 2x2 + x3 + x4 = comp_f_g[1](x4,x3,cons_x[1](x2,x1))
    
    rec[walk_0][1](Leaf(x1)) = 2x1 + 3 >= 2x1 = cons_x(x1)
   problem:
    cons_x[1](x2,x1) -> Cons(x2,x1)
    comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) -> cons_x[1](x4,comp_f_g[1](x3,x2,x1))
    comp_f_g[1](cons_x(x3),cons_x(x2),x1) -> cons_x[1](x3,cons_x[1](x2,x1))
    comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) -> comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
    comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) -> comp_f_g[1](x4,x3,cons_x[1](x2,x1))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [comp_f_g[1]](x0, x1, x2) = 2x0 + x1 + x2 + 5,
     
     [comp_f_g](x0, x1) = 4x0 + 2x1 + 5,
     
     [cons_x](x0) = 5x0 + 4,
     
     [Cons](x0, x1) = 4x0 + x1,
     
     [cons_x[1]](x0, x1) = 5x0 + x1 + 3
    orientation:
     cons_x[1](x2,x1) = x1 + 5x2 + 3 >= x1 + 4x2 = Cons(x2,x1)
     
     comp_f_g[1](cons_x(x4),comp_f_g(x3,x2),x1) = x1 + 2x2 + 4x3 + 10x4 + 18 >= x1 + x2 + 2x3 + 5x4 + 8 = cons_x[1](x4,comp_f_g[1](x3,x2,x1))
     
     comp_f_g[1](cons_x(x3),cons_x(x2),x1) = x1 + 5x2 + 10x3 + 17 >= x1 + 5x2 + 5x3 + 6 = cons_x[1](x3,cons_x[1](x2,x1))
     
     comp_f_g[1](comp_f_g(x5,x4),comp_f_g(x3,x2),x1) = x1 + 2x2 + 4x3 + 4x4 + 8x5 + 20 >= x1 + x2 + 2x3 + x4 + 2x5 + 10 = comp_f_g[1](x5,x4,comp_f_g[1](x3,x2,x1))
     
     comp_f_g[1](comp_f_g(x4,x3),cons_x(x2),x1) = x1 + 5x2 + 4x3 + 8x4 + 19 >= x1 + 5x2 + x3 + 2x4 + 8 = comp_f_g[1](x4,x3,cons_x[1](x2,x1))
    problem:
     
    Qed