YES

Problem:
 rec[iter_0][3](0()) -> id()
 rec[iter_0][3](S(x14)) -> compS_f(rec[iter_0][3](x14))
 compS_f[1](compS_f(x5),x3) -> compS_f[1](x5,S(x3))
 compS_f[1](id(),x7) -> S(x7)
 main(0()) -> 0()
 main(S(x25)) -> compS_f[1](rec[iter_0][3](x25),0())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [main](x0) = 2x0 + 2,
   
   [compS_f[1]](x0, x1) = 2x0 + 2x1 + 1,
   
   [compS_f](x0) = x0 + 4,
   
   [S](x0) = x0 + 4,
   
   [id] = 4,
   
   [rec[iter_0][3]](x0) = x0 + 2,
   
   [0] = 2
  orientation:
   rec[iter_0][3](0()) = 4 >= 4 = id()
   
   rec[iter_0][3](S(x14)) = x14 + 6 >= x14 + 6 = compS_f(rec[iter_0][3](x14))
   
   compS_f[1](compS_f(x5),x3) = 2x3 + 2x5 + 9 >= 2x3 + 2x5 + 9 = compS_f[1](x5,S(x3))
   
   compS_f[1](id(),x7) = 2x7 + 9 >= x7 + 4 = S(x7)
   
   main(0()) = 6 >= 2 = 0()
   
   main(S(x25)) = 2x25 + 10 >= 2x25 + 9 = compS_f[1](rec[iter_0][3](x25),0())
  problem:
   rec[iter_0][3](0()) -> id()
   rec[iter_0][3](S(x14)) -> compS_f(rec[iter_0][3](x14))
   compS_f[1](compS_f(x5),x3) -> compS_f[1](x5,S(x3))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [compS_f[1]](x0, x1) = x0 + x1 + 4,
    
    [compS_f](x0) = x0 + 4,
    
    [S](x0) = x0 + 4,
    
    [id] = 0,
    
    [rec[iter_0][3]](x0) = 7x0,
    
    [0] = 3
   orientation:
    rec[iter_0][3](0()) = 21 >= 0 = id()
    
    rec[iter_0][3](S(x14)) = 7x14 + 28 >= 7x14 + 4 = compS_f(rec[iter_0][3](x14))
    
    compS_f[1](compS_f(x5),x3) = x3 + x5 + 8 >= x3 + x5 + 8 = compS_f[1](x5,S(x3))
   problem:
    compS_f[1](compS_f(x5),x3) -> compS_f[1](x5,S(x3))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                            [1 0 1]     [1 0 0]  
     [compS_f[1]](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                            [0 0 0]     [0 0 0]  ,
     
                     [1 0 1]     [0]
     [compS_f](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [1],
     
               [1 0 0]  
     [S](x0) = [0 0 0]x0
               [0 0 0]  
    orientation:
                                  [1 0 0]     [1 0 1]     [1]    [1 0 0]     [1 0 1]                         
     compS_f[1](compS_f(x5),x3) = [0 0 0]x3 + [0 0 0]x5 + [0] >= [0 0 0]x3 + [0 0 0]x5 = compS_f[1](x5,S(x3))
                                  [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]                         
    problem:
     
    Qed