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

WORST_CASE(Omega(n^1),?)