Input TRS:
    1: +(x,0()) -> x
    2: +(x,s(y)) -> s(+(x,y))
    3: +(0(),y) -> y
    4: +(s(x),y) -> s(+(x,y))
    5: +(x,+(y,z)) -> +(+(x,y),z)
    6: f(g(f(x))) -> f(h(s(0()),x))
    7: f(g(h(x,y))) -> f(h(s(x),y))
    8: f(h(x,h(y,z))) -> f(h(+(x,y),z))
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 8 1 3 7 6
     h(x1,x2)	weight: (/ 47191 4) + 2 * x1 + x2
     s(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
     g(x1)	weight: 11798 + 2 * x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 5 2
     h(x1,x2)	weight: (/ 47191 4) + 2 * x1 + x2
     s(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 9865 4) + x1 + 2 * x2
     g(x1)	weight: 11798 + 2 * x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 4
     h(x1,x2)	weight: (/ 47191 4) + 2 * x1 + x2
     s(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 4) + 2 * x1 + x2
     g(x1)	weight: 11798 + 2 * x1
Number of strict rules: 0
YES