Input TRS:
    1: f(j(x,y),y) -> g(f(x,k(y)))
    2: f(x,h1(y,z)) -> h2(|0|(),x,h1(y,z))
    3: g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
    4: h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
    5: i(f(x,h(y))) -> y
    6: i(h2(s(x),y,h1(x,z))) -> z
    7: k(h(x)) -> h1(|0|(),x)
    8: k(h1(x,y)) -> h1(s(x),y)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 7 6 2
   |0|()	weight: 0
     h(x1)	weight: (/ 6937 8) + x1
     s(x1)	weight: (/ 99649 8) + x1
     k(x1)	weight: (/ 99649 4) + 2 * x1
     f(x1,x2)	weight: (/ 1 8) + 2 * x1 + x2
     j(x1,x2)	weight: (/ 298947 8) + x1 + x2
    h1(x1,x2)	weight: (/ 1 8) + 2 * x1 + 2 * x2
     i(x1)	weight: x1
    h2(x1,x2,x3)	weight: x1 + x2 + x3
     g(x1)	weight: (/ 49825 4) + x1
Number of strict rules: 0
YES