Input TRS:
    1: qsort(nil()) -> nil()
    2: qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
    3: lowers(x,nil()) -> nil()
    4: lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
    5: greaters(x,nil()) -> nil()
    6: greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #qsort(.(x,y)) -> #qsort(lowers(x,y))
   #2: #qsort(.(x,y)) -> #lowers(x,y)
   #3: #qsort(.(x,y)) -> #qsort(greaters(x,y))
   #4: #qsort(.(x,y)) -> #greaters(x,y)
   #5: #greaters(x,.(y,z)) -> #greaters(x,z)
   #6: #greaters(x,.(y,z)) -> #greaters(x,z)
   #7: #lowers(x,.(y,z)) -> #lowers(x,z)
   #8: #lowers(x,.(y,z)) -> #lowers(x,z)
Number of SCCs: 2, DPs: 4, edges: 8
	SCC { #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
lowers(x1,x2)	weight: 0
greaters(x1,x2)	weight: 0
    <=(x1,x2)	weight: 0
    ++(x1,x2)	weight: 0
 qsort(x1)	weight: 0
#qsort(x1)	weight: 0
    if(x1,x2,x3)	weight: 0
#lowers(x1,x2)	weight: x2
   nil()	weight: 0
#greaters(x1,x2)	weight: 0
     .(x1,x2)	weight: (/ 1 2) + x2
    Usable rules: { }
    Removed DPs: #7 #8
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #5 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
lowers(x1,x2)	weight: 0
greaters(x1,x2)	weight: 0
    <=(x1,x2)	weight: 0
    ++(x1,x2)	weight: 0
 qsort(x1)	weight: 0
#qsort(x1)	weight: 0
    if(x1,x2,x3)	weight: 0
#lowers(x1,x2)	weight: 0
   nil()	weight: 0
#greaters(x1,x2)	weight: x2
     .(x1,x2)	weight: (/ 1 2) + x2
    Usable rules: { }
    Removed DPs: #5 #6
Number of SCCs: 0, DPs: 0, edges: 0
YES