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