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