Input TRS:
    1: f(f(a(),x),a()) -> f(f(f(a(),f(a(),a())),x),a())
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆2_a(x,a()) -> f(f❆2_a(f❆1_a(a()),x),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(f❆1_a(a()),x),a())
   #3: #f❆2_a(x,a()) -> #f❆2_a(f❆1_a(a()),x)
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
f❆2_a(x1,x2)	weight: (/ 1 4)
#f❆2_a(x1,x2)	weight: (/ 1 2)
     f(x1,x2)	weight: (/ 1 4)
   #f(x1,x2)	weight: x1
f❆1_a(x1)	weight: (/ 3 4)
    Usable rules: { 1 3 }
    Removed DPs: #1 #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 3 8)
f❆2_a(x1,x2)	weight: 0
#f❆2_a(x1,x2)	weight: max{(/ 1 8) + x2, (/ 1 4) + x1}
     f(x1,x2)	weight: 0
   #f(x1,x2)	weight: 0
f❆1_a(x1)	weight: (/ 1 8)
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES