Input TRS:
    1: f(f(x)) -> f(x)
    2: f(s(x)) -> f(x)
    3: g(s(0())) -> g(f(s(0())))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 2
     s(x1)	weight: (/ 1 8) + x1
     f(x1)	weight: x1
     0()	weight: 0
     g(x1)	weight: x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(s(0())) -> #g(f(s(0())))
   #2: #g(s(0())) -> #f(s(0()))
Number of SCCs: 0, DPs: 0, edges: 0
YES