Input TRS:
    1: f(g(x)) -> f(a(g(g(f(x))),g(f(x))))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_g(x) -> f❆1_a(g(g(f(x))),g(f(x)))
2: f(a(_1,_2)) ->= f❆1_a(_1,_2)
3: f(g(_1)) ->= f❆1_g(_1)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(g(_1)) ->? #f❆1_g(_1)
   #2: #f❆1_g(x) -> #f(x)
   #3: #f❆1_g(x) -> #f(x)
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1,x2)	weight: 0
#f❆1_g(x1)	weight: (/ 1 4) + x1
f❆1_g(x1)	weight: 0
     f(x1)	weight: 0
   #f(x1)	weight: x1
f❆1_a(x1,x2)	weight: 0
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0, edges: 0
YES