* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys()) -> cons(x,append(xs,ys()))
            append(nil(),ys()) -> ys()
            filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs)
            filterhigh(n,nil()) -> nil()
            filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs)
            filterlow(n,nil()) -> nil()
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            get(n,cons(x,nil())) -> x
            get(n,nil()) -> 0()
            get(0(),cons(x,cons(y,xs))) -> x
            get(s(n),cons(x,cons(y,xs))) -> get(n,cons(y,xs))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if1(false(),n,x,xs) -> cons(x,filterlow(n,xs))
            if1(true(),n,x,xs) -> filterlow(n,xs)
            if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs))
            if2(true(),n,x,xs) -> filterhigh(n,xs)
            length(cons(x,xs)) -> s(length(xs))
            length(nil()) -> 0()
            qs(n,cons(x,xs)) -> append(qs(half(n),filterlow(get(n,cons(x,xs)),cons(x,xs)))
                                      ,cons(get(n,cons(x,xs)),qs(half(n),filterhigh(get(n,cons(x,xs)),cons(x,xs)))))
            qs(n,nil()) -> nil()
            qsort(xs) -> qs(half(length(xs)),xs)
        - Signature:
            {append/2,filterhigh/2,filterlow/2,ge/2,get/2,half/1,if1/4,if2/4,length/1,qs/2,qsort/1} / {0/0,cons/2
            ,false/0,nil/0,s/1,true/0,ys/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,get,half,if1,if2,length,qs
            ,qsort} and constructors {0,cons,false,nil,s,true,ys}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys()) -> cons(x,append(xs,ys()))
            append(nil(),ys()) -> ys()
            filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs)
            filterhigh(n,nil()) -> nil()
            filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs)
            filterlow(n,nil()) -> nil()
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            get(n,cons(x,nil())) -> x
            get(n,nil()) -> 0()
            get(0(),cons(x,cons(y,xs))) -> x
            get(s(n),cons(x,cons(y,xs))) -> get(n,cons(y,xs))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if1(false(),n,x,xs) -> cons(x,filterlow(n,xs))
            if1(true(),n,x,xs) -> filterlow(n,xs)
            if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs))
            if2(true(),n,x,xs) -> filterhigh(n,xs)
            length(cons(x,xs)) -> s(length(xs))
            length(nil()) -> 0()
            qs(n,cons(x,xs)) -> append(qs(half(n),filterlow(get(n,cons(x,xs)),cons(x,xs)))
                                      ,cons(get(n,cons(x,xs)),qs(half(n),filterhigh(get(n,cons(x,xs)),cons(x,xs)))))
            qs(n,nil()) -> nil()
            qsort(xs) -> qs(half(length(xs)),xs)
        - Signature:
            {append/2,filterhigh/2,filterlow/2,ge/2,get/2,half/1,if1/4,if2/4,length/1,qs/2,qsort/1} / {0/0,cons/2
            ,false/0,nil/0,s/1,true/0,ys/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,filterhigh,filterlow,ge,get,half,if1,if2,length,qs
            ,qsort} and constructors {0,cons,false,nil,s,true,ys}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          append(y,ys()){y -> cons(x,y)} =
            append(cons(x,y),ys()) ->^+ cons(x,append(y,ys()))
              = C[append(y,ys()) = append(y,ys()){}]

WORST_CASE(Omega(n^1),?)