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