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