Input TRS:
    1: f(x,f(a(),a())) -> f(a(),f(f(f(a(),a()),a()),x))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(x,f(a(),a())) -> #f(a(),f(f(f(a(),a()),a()),x))
   #2: #f(x,f(a(),a())) -> #f(f(f(a(),a()),a()),x)
   #3: #f(x,f(a(),a())) -> #f(f(a(),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)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... succeeded.
     a()	weight: (/ 17 16); (- (/ 1 16))
     f(x1,x2)	weight: max{0, (- (/ 1 2)) + x2_2 + x1_1 + x1_2}; (- (/ 5 16)) + x2_2 + x1_2
   #f(x1,x2)	weight: max{0, (/ 1 2) + x2_1 + x2_2 + x1_1}; x2_2 + x1_2
    Usable rules: { 1 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     a()	weight: (/ 7 4)
     f(x1,x2)	weight: max{0, (- (/ 9 4)) + x2 + x1}
   #f(x1,x2)	weight: max{0, -1 + x2 + x1}
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES