* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(minus(x,y),z) -> minus(x,plus(y,z))
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(0(),y) -> y
            plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),y) -> s(plus(x,y))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
            sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
            sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {app/2,gt/2,id/1,if/3,minus/2,not/1,plus/2,quot/2,sum/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,zero/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,gt,id,if,minus,not,plus,quot,sum} and constructors {0
            ,cons,false,nil,s,true,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(minus(x,y),z) -> minus(x,plus(y,z))
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(0(),y) -> y
            plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),y) -> s(plus(x,y))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
            sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
            sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {app/2,gt/2,id/1,if/3,minus/2,not/1,plus/2,quot/2,sum/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,zero/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,gt,id,if,minus,not,plus,quot,sum} and constructors {0
            ,cons,false,nil,s,true,zero}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> cons(x,y)} =
            app(cons(x,y),z) ->^+ cons(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)