Input TRS:
    1: f(0()) -> 1()
    2: f(s(x)) -> g(x,s(x))
    3: g(0(),y) -> y
    4: g(s(x),y) -> g(x,+(y,s(x)))
    5: +(x,0()) -> x
    6: +(x,s(y)) -> s(+(x,y))
    7: g(s(x),y) -> g(x,s(+(y,x)))
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(s(x)) -> #g(x,s(x))
   #2: #+(x,s(y)) -> #+(x,y)
   #3: #g(s(x),y) -> #g(x,s(+(y,x)))
   #4: #g(s(x),y) -> #+(y,x)
   #5: #g(s(x),y) -> #g(x,+(y,s(x)))
   #6: #g(s(x),y) -> #+(y,s(x))
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #2 }
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: 0
   #g(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
     g(x1,x2)	weight: 0
   #+(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
     s(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: 0
     0()	weight: 0
   #f(x1)	weight: 0
   #g(x1,x2)	weight: x1
     +(x1,x2)	weight: (/ 1 4)
     g(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3 #5
Number of SCCs: 0, DPs: 0, edges: 0
YES