YES

Problem:
 comp_f_g[1](walk_1(),walk_4(x11),x7) -> walk_4[1](x11,x7)
 comp_f_g[1](comp_f_g(x7,walk_4(x9)),walk_4(x5),x3) -> comp_f_g[1](x7,walk_4(x9),walk_4[1](x5,x3))
 walk_4[1](x7,x11) -> Cons(x7,x11)
 rec[walk_0][1](Nil()) -> walk_1()
 rec[walk_0][1](Cons(x61,x77)) -> comp_f_g(rec[walk_0][1](x77),walk_4(x61))
 main(Nil()) -> Nil()
 main(Cons(x122,x154)) -> comp_f_g[1](rec[walk_0][1](x154),walk_4(x122),Nil())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [main](x0) = 6x0,
   
   [rec[walk_0][1]](x0) = 5x0 + 2,
   
   [Nil] = 1,
   
   [Cons](x0, x1) = 4x0 + x1 + 2,
   
   [comp_f_g](x0, x1) = x0 + x1 + 1,
   
   [walk_4[1]](x0, x1) = 4x0 + x1 + 2,
   
   [comp_f_g[1]](x0, x1, x2) = x0 + x1 + x2 + 1,
   
   [walk_4](x0) = 4x0 + 1,
   
   [walk_1] = 0
  orientation:
   comp_f_g[1](walk_1(),walk_4(x11),x7) = 4x11 + x7 + 2 >= 4x11 + x7 + 2 = walk_4[1](x11,x7)
   
   comp_f_g[1](comp_f_g(x7,walk_4(x9)),walk_4(x5),x3) = x3 + 4x5 + x7 + 4x9 + 4 >= x3 + 4x5 + x7 + 4x9 + 4 = comp_f_g[1](x7,walk_4(x9),walk_4[1](x5,x3))
   
   walk_4[1](x7,x11) = x11 + 4x7 + 2 >= x11 + 4x7 + 2 = Cons(x7,x11)
   
   rec[walk_0][1](Nil()) = 7 >= 0 = walk_1()
   
   rec[walk_0][1](Cons(x61,x77)) = 20x61 + 5x77 + 12 >= 4x61 + 5x77 + 4 = comp_f_g(rec[walk_0][1](x77),walk_4(x61))
   
   main(Nil()) = 6 >= 1 = Nil()
   
   main(Cons(x122,x154)) = 24x122 + 6x154 + 12 >= 4x122 + 5x154 + 5 = comp_f_g[1](rec[walk_0][1](x154),walk_4(x122),Nil())
  problem:
   comp_f_g[1](walk_1(),walk_4(x11),x7) -> walk_4[1](x11,x7)
   comp_f_g[1](comp_f_g(x7,walk_4(x9)),walk_4(x5),x3) ->
   comp_f_g[1](x7,walk_4(x9),walk_4[1](x5,x3))
   walk_4[1](x7,x11) -> Cons(x7,x11)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [Cons](x0, x1) = x0 + x1,
    
    [comp_f_g](x0, x1) = 2x0 + 4x1 + 1,
    
    [walk_4[1]](x0, x1) = x0 + x1,
    
    [comp_f_g[1]](x0, x1, x2) = 2x0 + 4x1 + 2x2 + 2,
    
    [walk_4](x0) = 2x0 + 2,
    
    [walk_1] = 3
   orientation:
    comp_f_g[1](walk_1(),walk_4(x11),x7) = 8x11 + 2x7 + 16 >= x11 + x7 = walk_4[1](x11,x7)
    
    comp_f_g[1](comp_f_g(x7,walk_4(x9)),walk_4(x5),x3) = 2x3 + 8x5 + 4x7 + 16x9 + 28 >= 2x3 + 2x5 + 2x7 + 8x9 + 10 = comp_f_g[1](x7,walk_4(x9),walk_4[1](x5,x3))
    
    walk_4[1](x7,x11) = x11 + x7 >= x11 + x7 = Cons(x7,x11)
   problem:
    walk_4[1](x7,x11) -> Cons(x7,x11)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 0 0]     [1 0 0]  
     [Cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 0 0]  ,
     
                           [1 0 0]     [1 0 0]     [1]
     [walk_4[1]](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                           [0 0 1]     [0 0 0]     [0]
    orientation:
                         [1 0 0]      [1 0 0]     [1]    [1 0 0]      [1 0 0]                 
     walk_4[1](x7,x11) = [0 0 0]x11 + [0 0 0]x7 + [0] >= [0 0 0]x11 + [0 0 0]x7 = Cons(x7,x11)
                         [0 0 0]      [0 0 1]     [0]    [0 0 0]      [0 0 0]                 
    problem:
     
    Qed