Input TRS:
    1: -(x,0()) -> x
    2: -(0(),s(y)) -> 0()
    3: -(s(x),s(y)) -> -(x,y)
    4: f(0()) -> 0()
    5: f(s(x)) -> -(s(x),g(f(x)))
    6: g(0()) -> s(0())
    7: g(s(x)) -> -(s(x),f(g(x)))
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(s(x)) -> #-(s(x),f(g(x)))
   #2: #g(s(x)) -> #f(g(x))
   #3: #g(s(x)) -> #g(x)
   #4: #f(s(x)) -> #-(s(x),g(f(x)))
   #5: #f(s(x)) -> #g(f(x))
   #6: #f(s(x)) -> #f(x)
   #7: #-(s(x),s(y)) -> #-(x,y)
Number of SCCs: 2, DPs: 5, edges: 9
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
     f(x1)	weight: 0
     0()	weight: 0
     -(x1,x2)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: 0
   #-(x1,x2)	weight: x2
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 4, edges: 8
	SCC { #2 #3 #5 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 3 2) + x1
     f(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
     -(x1,x2)	weight: x1
   #f(x1)	weight: x1
   #g(x1)	weight: (/ 1 2) + x1
   #-(x1,x2)	weight: 0
     g(x1)	weight: (/ 3 2) + x1
    Usable rules: { 1..7 }
    Removed DPs: #2 #3 #5 #6
Number of SCCs: 0, DPs: 0, edges: 0
YES