Input TRS:
    1: a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
    2: f(a(x),a(y)) -> a(f(x,y))
    3: f(b(x),b(y)) -> b(f(x,y))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(a(x),a(y)) -> #a(f(x,y))
   #2: #f(a(x),a(y)) -> #f(x,y)
   #3: #f(b(x),b(y)) -> #f(x,y)
   #4: #a(a(f(x,y))) -> #f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
   #5: #a(a(f(x,y))) -> #a(b(a(b(a(x)))))
   #6: #a(a(f(x,y))) -> #a(b(a(x)))
   #7: #a(a(f(x,y))) -> #a(x)
   #8: #a(a(f(x,y))) -> #a(b(a(b(a(y)))))
   #9: #a(a(f(x,y))) -> #a(b(a(y)))
   #10: #a(a(f(x,y))) -> #a(y)
Number of SCCs: 1, DPs: 6, edges: 17
	SCC { #1..4 #7 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: x1
     b(x1)	weight: x1
     f(x1,x2)	weight: (/ 1 2) + x1 + x2
   #f(x1,x2)	weight: (/ 1 2) + x1 + x2
   #a(x1)	weight: x1
    Usable rules: { 1..3 }
    Removed DPs: #7 #10
Number of SCCs: 1, DPs: 4, edges: 9
	SCC { #1..4 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a(x1)	weight: (/ 3 4); x1_1 + x1_2
     b(x1)	weight: (/ 1 8); (/ 1 8) + x1_2
     f(x1,x2)	weight: x1_1; (/ 1 8) + x1_2
   #f(x1,x2)	weight: (/ 1 4) + x1_2; 0
   #a(x1)	weight: x1_1 + x1_2; 0
    Usable rules: { 1..3 }
    Removed DPs: #1 #3 #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a(x1)	weight: (/ 1 8) + x1
     b(x1)	weight: (/ 1 4)
     f(x1,x2)	weight: (/ 1 8) + x1
   #f(x1,x2)	weight: x1
   #a(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES