* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Nil(),ys) -> Nil()
            goal(xs,ys) -> addlist(xs,ys)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} and constructors {0,Cons,False,Nil
            ,S,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Nil(),ys) -> Nil()
            goal(xs,ys) -> addlist(xs,ys)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} and constructors {0,Cons,False,Nil
            ,S,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          addlist(y,z){y -> Cons(x,y),z -> Cons(S(0()),z)} =
            addlist(Cons(x,y),Cons(S(0()),z)) ->^+ Cons(S(x),addlist(y,z))
              = C[addlist(y,z) = addlist(y,z){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Nil(),ys) -> Nil()
            goal(xs,ys) -> addlist(xs,ys)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} and constructors {0,Cons,False,Nil
            ,S,True}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          Cons_0(2,2) -> 2
          Cons_1(3,4) -> 1
          Cons_1(3,4) -> 4
          False_0() -> 2
          False_1() -> 1
          Nil_0() -> 2
          Nil_1() -> 1
          Nil_1() -> 4
          S_0(2) -> 2
          S_1(2) -> 3
          True_0() -> 2
          True_1() -> 1
          addlist_0(2,2) -> 1
          addlist_1(2,2) -> 1
          addlist_1(2,2) -> 4
          goal_0(2,2) -> 1
          notEmpty_0(2) -> 1
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Nil(),ys) -> Nil()
            goal(xs,ys) -> addlist(xs,ys)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} and constructors {0,Cons,False,Nil
            ,S,True}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))