Input TRS:
    1: f(a(),f(x,a())) -> f(a(),f(a(),f(f(a(),a()),x)))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(a(),f(x,a())) -> #f(a(),f(a(),f(f(a(),a()),x)))
   #2: #f(a(),f(x,a())) -> #f(a(),f(f(a(),a()),x))
   #3: #f(a(),f(x,a())) -> #f(f(a(),a()),x)
   #4: #f(a(),f(x,a())) -> #f(a(),a())
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #1 #2 }
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 8); (/ 1 8)
     f(x1,x2)	weight: (/ 1 8) + x2_2 + x1_2; 0
   #f(x1,x2)	weight: x2_1; 0
    Usable rules: { 1 }
    Removed DPs: #2
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 8); (/ 1 4)
     f(x1,x2)	weight: (/ 1 8) + x2_2; (/ 1 8)
   #f(x1,x2)	weight: x2_1; 0
    Usable rules: { 1 }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES