* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__dbl(X)) -> dbl(activate(X))
            activate(n__dbls(X)) -> dbls(activate(X))
            activate(n__from(X)) -> from(X)
            activate(n__indx(X1,X2)) -> indx(activate(X1),X2)
            activate(n__s(X)) -> s(X)
            activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
            dbl(X) -> n__dbl(X)
            dbl(0()) -> 0()
            dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
            dbl1(0()) -> 01()
            dbl1(s(X)) -> s1(s1(dbl1(activate(X))))
            dbls(X) -> n__dbls(X)
            dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
            dbls(nil()) -> nil()
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            indx(X1,X2) -> n__indx(X1,X2)
            indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
            indx(nil(),X) -> nil()
            quote(0()) -> 01()
            quote(dbl(X)) -> dbl1(X)
            quote(s(X)) -> s1(quote(activate(X)))
            quote(sel(X,Y)) -> sel1(X,Y)
            s(X) -> n__s(X)
            sel(X1,X2) -> n__sel(X1,X2)
            sel(0(),cons(X,Y)) -> activate(X)
            sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
            sel1(0(),cons(X,Y)) -> activate(X)
            sel1(s(X),cons(Y,Z)) -> sel1(activate(X),activate(Z))
        - Signature:
            {activate/1,dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,s/1,sel/2,sel1/2} / {0/0,01/0,cons/2,n__dbl/1
            ,n__dbls/1,n__from/1,n__indx/2,n__s/1,n__sel/2,nil/0,s1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,dbl,dbl1,dbls,from,indx,quote,s,sel
            ,sel1} and constructors {0,01,cons,n__dbl,n__dbls,n__from,n__indx,n__s,n__sel,nil,s1}
    + 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__dbl(X)) -> dbl(activate(X))
            activate(n__dbls(X)) -> dbls(activate(X))
            activate(n__from(X)) -> from(X)
            activate(n__indx(X1,X2)) -> indx(activate(X1),X2)
            activate(n__s(X)) -> s(X)
            activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
            dbl(X) -> n__dbl(X)
            dbl(0()) -> 0()
            dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
            dbl1(0()) -> 01()
            dbl1(s(X)) -> s1(s1(dbl1(activate(X))))
            dbls(X) -> n__dbls(X)
            dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y)))
            dbls(nil()) -> nil()
            from(X) -> cons(activate(X),n__from(n__s(activate(X))))
            from(X) -> n__from(X)
            indx(X1,X2) -> n__indx(X1,X2)
            indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z)))
            indx(nil(),X) -> nil()
            quote(0()) -> 01()
            quote(dbl(X)) -> dbl1(X)
            quote(s(X)) -> s1(quote(activate(X)))
            quote(sel(X,Y)) -> sel1(X,Y)
            s(X) -> n__s(X)
            sel(X1,X2) -> n__sel(X1,X2)
            sel(0(),cons(X,Y)) -> activate(X)
            sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z))
            sel1(0(),cons(X,Y)) -> activate(X)
            sel1(s(X),cons(Y,Z)) -> sel1(activate(X),activate(Z))
        - Signature:
            {activate/1,dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,s/1,sel/2,sel1/2} / {0/0,01/0,cons/2,n__dbl/1
            ,n__dbls/1,n__from/1,n__indx/2,n__s/1,n__sel/2,nil/0,s1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,dbl,dbl1,dbls,from,indx,quote,s,sel
            ,sel1} and constructors {0,01,cons,n__dbl,n__dbls,n__from,n__indx,n__s,n__sel,nil,s1}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__dbl(x)} =
            activate(n__dbl(x)) ->^+ dbl(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)