Input TRS:
    1: f(x,f(y,a())) -> f(f(f(f(a(),x),y),a()),h(a()))
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(x,f(y,a())) -> #f(f(f(f(a(),x),y),a()),h(a()))
   #2: #f(x,f(y,a())) -> #f(f(f(a(),x),y),a())
   #3: #f(x,f(y,a())) -> #f(f(a(),x),y)
   #4: #f(x,f(y,a())) -> #f(a(),x)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #3 #4 }
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: (/ 1 8); 0
     h(x1)	weight: (max (- (/ 1 8)) 0); -1
     f(x1,x2)	weight: max{0, (/ 3 8) + x2_1 + x2_2 + x1_1}; (- (/ 1 8))
   #f(x1,x2)	weight: max{0, (/ 1 8) + x2_1 + x1_1}; 0
    Usable rules: { 1 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     h(x1)	weight: (/ 1 2)
     f(x1,x2)	weight: (/ 1 2) + x1
   #f(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES