* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
            a__dbl(X) -> dbl(X)
            a__dbl(0()) -> 0()
            a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
            a__first(X1,X2) -> first(X1,X2)
            a__first(0(),X) -> nil()
            a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
            a__sqr(X) -> sqr(X)
            a__sqr(0()) -> 0()
            a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)),a__dbl(mark(X))))
            a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
            a__terms(X) -> terms(X)
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(dbl(X)) -> a__dbl(mark(X))
            mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
            mark(nil()) -> nil()
            mark(recip(X)) -> recip(mark(X))
            mark(s(X)) -> s(mark(X))
            mark(sqr(X)) -> a__sqr(mark(X))
            mark(terms(X)) -> a__terms(mark(X))
        - Signature:
            {a__add/2,a__dbl/1,a__first/2,a__sqr/1,a__terms/1,mark/1} / {0/0,add/2,cons/2,dbl/1,first/2,nil/0,recip/1
            ,s/1,sqr/1,terms/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__add,a__dbl,a__first,a__sqr,a__terms
            ,mark} and constructors {0,add,cons,dbl,first,nil,recip,s,sqr,terms}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
            a__dbl(X) -> dbl(X)
            a__dbl(0()) -> 0()
            a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
            a__first(X1,X2) -> first(X1,X2)
            a__first(0(),X) -> nil()
            a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
            a__sqr(X) -> sqr(X)
            a__sqr(0()) -> 0()
            a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)),a__dbl(mark(X))))
            a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
            a__terms(X) -> terms(X)
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(dbl(X)) -> a__dbl(mark(X))
            mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
            mark(nil()) -> nil()
            mark(recip(X)) -> recip(mark(X))
            mark(s(X)) -> s(mark(X))
            mark(sqr(X)) -> a__sqr(mark(X))
            mark(terms(X)) -> a__terms(mark(X))
        - Signature:
            {a__add/2,a__dbl/1,a__first/2,a__sqr/1,a__terms/1,mark/1} / {0/0,add/2,cons/2,dbl/1,first/2,nil/0,recip/1
            ,s/1,sqr/1,terms/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__add,a__dbl,a__first,a__sqr,a__terms
            ,mark} and constructors {0,add,cons,dbl,first,nil,recip,s,sqr,terms}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> add(x,y)} =
            mark(add(x,y)) ->^+ a__add(mark(x),mark(y))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)