YES

Problem:
 f(j(x,y),y) -> g(f(x,k(y)))
 f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
 g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
 h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
 i(f(x,h(y))) -> y
 i(h2(s(x),y,h1(x,z))) -> z
 k(h(x)) -> h1(0(),x)
 k(h1(x,y)) -> h1(s(x),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [i](x0) = 2x0 + 2,
   
   [h](x0) = 5x0 + 1,
   
   [s](x0) = x0 + 1,
   
   [h2](x0, x1, x2) = x0 + x1 + x2 + 2,
   
   [0] = 0,
   
   [h1](x0, x1) = x0 + x1 + 5,
   
   [g](x0) = x0 + 7,
   
   [k](x0) = 4x0 + 1,
   
   [f](x0, x1) = 6x0 + 2x1 + 7,
   
   [j](x0, x1) = 3x0 + x1 + 3
  orientation:
   f(j(x,y),y) = 18x + 8y + 25 >= 6x + 8y + 16 = g(f(x,k(y)))
   
   f(x,h1(y,z)) = 6x + 2y + 2z + 17 >= x + y + z + 7 = h2(0(),x,h1(y,z))
   
   g(h2(x,y,h1(z,u))) = u + x + y + z + 14 >= u + x + y + z + 8 = h2(s(x),y,h1(z,u))
   
   h2(x,j(y,h1(z,u)),h1(z,u)) = 2u + x + 3y + 2z + 15 >= u + x + y + z + 9 = h2(s(x),y,h1(s(z),u))
   
   i(f(x,h(y))) = 12x + 20y + 20 >= y = y
   
   i(h2(s(x),y,h1(x,z))) = 4x + 2y + 2z + 18 >= z = z
   
   k(h(x)) = 20x + 5 >= x + 5 = h1(0(),x)
   
   k(h1(x,y)) = 4x + 4y + 21 >= x + y + 6 = h1(s(x),y)
  problem:
   k(h(x)) -> h1(0(),x)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
          [0]
    [0] = [0]
          [0],
    
                   [1 0 0]     [1 0 0]  
    [h1](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
    
              [1 0 1]  
    [k](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
              [1 0 0]    [1]    [1 0 0]             
    k(h(x)) = [0 0 0]x + [0] >= [0 0 0]x = h1(0(),x)
              [0 0 0]    [0]    [0 0 0]             
   problem:
    
   Qed