Input TRS:
    1: f(a(),f(b(),x)) -> f(a(),f(a(),f(a(),x)))
    2: f(b(),f(a(),x)) -> f(b(),f(b(),f(b(),x)))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_a(f❆1_b(x)) -> f❆1_a(f❆1_a(f❆1_a(x)))
2: f❆1_b(f❆1_a(x)) -> f❆1_b(f❆1_b(f❆1_b(x)))
3: f(a(),_1) ->= f❆1_a(_1)
4: f(b(),_1) ->= f❆1_b(_1)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 4 3
     a()	weight: 0
     b()	weight: 0
     f(x1,x2)	weight: (/ 1 2) + x1 + x2
f❆1_b(x1)	weight: x1
f❆1_a(x1)	weight: x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f❆1_b(f❆1_a(x)) -> #f❆1_b(f❆1_b(f❆1_b(x)))
   #2: #f❆1_b(f❆1_a(x)) -> #f❆1_b(f❆1_b(x))
   #3: #f❆1_b(f❆1_a(x)) -> #f❆1_b(x)
   #4: #f❆1_a(f❆1_b(x)) -> #f❆1_a(f❆1_a(f❆1_a(x)))
   #5: #f❆1_a(f❆1_b(x)) -> #f❆1_a(f❆1_a(x))
   #6: #f❆1_a(f❆1_b(x)) -> #f❆1_a(x)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
#f❆1_b(x1)	weight: 0
     f(x1,x2)	weight: 0
#f❆1_a(x1)	weight: x1
f❆1_b(x1)	weight: (/ 1 2) + x1
f❆1_a(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
#f❆1_b(x1)	weight: x1
     f(x1,x2)	weight: 0
#f❆1_a(x1)	weight: 0
f❆1_b(x1)	weight: (/ 1 2)
f❆1_a(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES