Input TRS:
    1: f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(f(x,a()),y) -> #f(f(a(),y),f(a(),x))
   #2: #f(f(x,a()),y) -> #f(a(),y)
   #3: #f(f(x,a()),y) -> #f(a(),x)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a()	weight: (/ 1 4); (/ 1 4)
     f(x1,x2)	weight: 0; (/ 1 4) + x2_1
   #f(x1,x2)	weight: x2_1 + x1_2; x2_1
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES