* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),X2)
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__from(X)) -> from(X)
            activate(n__s(X)) -> s(X)
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> activate(X)
            add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
            and(false(),Y) -> false()
            and(true(),X) -> activate(X)
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            s(X) -> n__s(X)
        - Signature:
            {activate/1,add/2,and/2,first/2,from/1,if/3,s/1} / {0/0,cons/2,false/0,n__add/2,n__first/2,n__from/1,n__s/1
            ,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,add,and,first,from,if,s} and constructors {0
            ,cons,false,n__add,n__first,n__from,n__s,nil,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),X2)
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__from(X)) -> from(X)
            activate(n__s(X)) -> s(X)
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> activate(X)
            add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
            and(false(),Y) -> false()
            and(true(),X) -> activate(X)
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> activate(X)
            s(X) -> n__s(X)
        - Signature:
            {activate/1,add/2,and/2,first/2,from/1,if/3,s/1} / {0/0,cons/2,false/0,n__add/2,n__first/2,n__from/1,n__s/1
            ,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,add,and,first,from,if,s} and constructors {0
            ,cons,false,n__add,n__first,n__from,n__s,nil,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__add(x,y)} =
            activate(n__add(x,y)) ->^+ add(activate(x),y)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)