Input TRS:
    1: f(x,0()) -> s(0())
    2: f(s(x),s(y)) -> s(f(x,y))
    3: g(0(),x) -> g(f(x,x),x)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x),s(y)) -> #f(x,y)
   #2: #g(0(),x) -> #g(f(x,x),x)
   #3: #g(0(),x) -> #f(x,x)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
     f(x1,x2)	weight: 0
     0()	weight: 0
   #f(x1,x2)	weight: x2
   #g(x1,x2)	weight: 0
     g(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES