Input TRS:
    1: f(x,y) -> x
    2: g(a()) -> h(a(),b(),a())
    3: i(x) -> f(x,x)
    4: h(x,x,y) -> g(x)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 1 3
     a()	weight: 0
     h(x1,x2,x3)	weight: 2 * x1 + 2 * x2 + x3
     b()	weight: 0
     f(x1,x2)	weight: (/ 1 4) + x1 + x2
     i(x1)	weight: (/ 1 2) + 2 * x1
     g(x1)	weight: 2 * x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(a()) -> #h(a(),b(),a())
   #2: #h(x,x,y) -> #g(x)
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 1 2)
     h(x1,x2,x3)	weight: 0
     b()	weight: 0
     f(x1,x2)	weight: 0
   #h(x1,x2,x3)	weight: max{0, (/ 1 2) + x2, (/ 1 4) + x1}
   #g(x1)	weight: (/ 1 4) + x1
     i(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES