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:
 DP Processor:
  DPs:
   f#(j(x,y),y) -> k#(y)
   f#(j(x,y),y) -> f#(x,k(y))
   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))
  TRS:
   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)
  Usable Rule Processor:
   DPs:
    f#(j(x,y),y) -> k#(y)
    f#(j(x,y),y) -> f#(x,k(y))
    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))
   TRS:
    k(h(x)) -> h1(0(),x)
    k(h1(x,y)) -> h1(s(x),y)
    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))
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     k(h(x)) -> h1(0(),x)
     k(h1(x,y)) -> h1(s(x),y)
     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))
    interpretation:
     [h2#](x0, x1, x2) = x1 + x2 + 0,
     
     [g#](x0) = x0 + 1,
     
     [k#](x0) = x0,
     
     [f#](x0, x1) = 1x0 + x1 + 1,
     
     [h](x0) = 2x0 + 6,
     
     [s](x0) = 0,
     
     [h2](x0, x1, x2) = x0 + 1x1 + x2 + 0,
     
     [0] = 0,
     
     [h1](x0, x1) = 0,
     
     [g](x0) = 1x0 + 2,
     
     [k](x0) = x0 + 1,
     
     [f](x0, x1) = 2x0 + 1,
     
     [j](x0, x1) = 2x0 + x1 + 1
    orientation:
     f#(j(x,y),y) = 3x + 1y + 2 >= y = k#(y)
     
     f#(j(x,y),y) = 3x + 1y + 2 >= 1x + y + 1 = f#(x,k(y))
     
     f#(j(x,y),y) = 3x + 1y + 2 >= 2x + 1 = g#(f(x,k(y)))
     
     f#(x,h1(y,z)) = 1x + 1 >= x + 0 = h2#(0(),x,h1(y,z))
     
     g#(h2(x,y,h1(z,u))) = x + 1y + 1 >= y + 0 = h2#(s(x),y,h1(z,u))
     
     h2#(x,j(y,h1(z,u)),h1(z,u)) = 2y + 1 >= y + 0 = h2#(s(x),y,h1(s(z),u))
     
     k(h(x)) = 2x + 6 >= 0 = h1(0(),x)
     
     k(h1(x,y)) = 1 >= 0 = h1(s(x),y)
     
     f(j(x,y),y) = 4x + 2y + 3 >= 3x + 2 = g(f(x,k(y)))
     
     f(x,h1(y,z)) = 2x + 1 >= 1x + 0 = h2(0(),x,h1(y,z))
     
     g(h2(x,y,h1(z,u))) = 1x + 2y + 2 >= 1y + 0 = h2(s(x),y,h1(z,u))
     
     h2(x,j(y,h1(z,u)),h1(z,u)) = x + 3y + 2 >= 1y + 0 = h2(s(x),y,h1(s(z),u))
    problem:
     DPs:
      
     TRS:
      k(h(x)) -> h1(0(),x)
      k(h1(x,y)) -> h1(s(x),y)
      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))
    Qed