Input TRS:
    1: f(0()) -> 1()
    2: f(s(x)) -> g(f(x))
    3: g(x) -> +(x,s(x))
    4: f(s(x)) -> +(f(x),s(f(x)))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x)) -> #g(f(x))
   #2: #f(s(x)) -> #f(x)
   #3: #f(s(x)) -> #f(x)
   #4: #f(s(x)) -> #f(x)
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #2..4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     f(x1)	weight: 0
     0()	weight: 0
   #f(x1)	weight: x1
   #g(x1)	weight: 0
     +(x1,x2)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2..4
Number of SCCs: 0, DPs: 0, edges: 0
YES