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