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