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

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,XS))) -> mark(XS)
            active(zeros()) -> mark(cons(0(),zeros()))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(tail(X)) -> tail(proper(X))
            proper(zeros()) -> ok(zeros())
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok
            ,zeros}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 5.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 11
          0_2() -> 18
          0_3() -> 27
          active_0(1) -> 2
          active_0(4) -> 2
          active_0(5) -> 2
          active_0(9) -> 2
          active_1(1) -> 15
          active_1(4) -> 15
          active_1(5) -> 15
          active_1(9) -> 15
          active_2(11) -> 16
          active_2(12) -> 16
          active_3(26) -> 22
          active_4(18) -> 28
          active_4(29) -> 30
          active_5(27) -> 31
          cons_0(1,1) -> 3
          cons_0(1,4) -> 3
          cons_0(1,5) -> 3
          cons_0(1,9) -> 3
          cons_0(4,1) -> 3
          cons_0(4,4) -> 3
          cons_0(4,5) -> 3
          cons_0(4,9) -> 3
          cons_0(5,1) -> 3
          cons_0(5,4) -> 3
          cons_0(5,5) -> 3
          cons_0(5,9) -> 3
          cons_0(9,1) -> 3
          cons_0(9,4) -> 3
          cons_0(9,5) -> 3
          cons_0(9,9) -> 3
          cons_1(1,1) -> 13
          cons_1(1,4) -> 13
          cons_1(1,5) -> 13
          cons_1(1,9) -> 13
          cons_1(4,1) -> 13
          cons_1(4,4) -> 13
          cons_1(4,5) -> 13
          cons_1(4,9) -> 13
          cons_1(5,1) -> 13
          cons_1(5,4) -> 13
          cons_1(5,5) -> 13
          cons_1(5,9) -> 13
          cons_1(9,1) -> 13
          cons_1(9,4) -> 13
          cons_1(9,5) -> 13
          cons_1(9,9) -> 13
          cons_1(11,12) -> 10
          cons_2(18,19) -> 17
          cons_2(20,21) -> 16
          cons_3(18,19) -> 26
          cons_3(23,24) -> 22
          cons_4(27,25) -> 29
          cons_4(28,19) -> 22
          cons_5(31,25) -> 30
          mark_0(1) -> 4
          mark_0(4) -> 4
          mark_0(5) -> 4
          mark_0(9) -> 4
          mark_1(10) -> 2
          mark_1(10) -> 15
          mark_1(13) -> 3
          mark_1(13) -> 13
          mark_1(14) -> 7
          mark_1(14) -> 14
          mark_2(17) -> 16
          ok_0(1) -> 5
          ok_0(4) -> 5
          ok_0(5) -> 5
          ok_0(9) -> 5
          ok_1(11) -> 6
          ok_1(11) -> 15
          ok_1(12) -> 6
          ok_1(12) -> 15
          ok_1(13) -> 3
          ok_1(13) -> 13
          ok_1(14) -> 7
          ok_1(14) -> 14
          ok_2(18) -> 20
          ok_2(19) -> 21
          ok_3(25) -> 24
          ok_3(26) -> 16
          ok_3(27) -> 23
          ok_4(29) -> 22
          proper_0(1) -> 6
          proper_0(4) -> 6
          proper_0(5) -> 6
          proper_0(9) -> 6
          proper_1(1) -> 15
          proper_1(4) -> 15
          proper_1(5) -> 15
          proper_1(9) -> 15
          proper_2(10) -> 16
          proper_2(11) -> 20
          proper_2(12) -> 21
          proper_3(17) -> 22
          proper_3(18) -> 23
          proper_3(19) -> 24
          tail_0(1) -> 7
          tail_0(4) -> 7
          tail_0(5) -> 7
          tail_0(9) -> 7
          tail_1(1) -> 14
          tail_1(4) -> 14
          tail_1(5) -> 14
          tail_1(9) -> 14
          top_0(1) -> 8
          top_0(4) -> 8
          top_0(5) -> 8
          top_0(9) -> 8
          top_1(15) -> 8
          top_2(16) -> 8
          top_3(22) -> 8
          top_4(30) -> 8
          zeros_0() -> 9
          zeros_1() -> 12
          zeros_2() -> 19
          zeros_3() -> 25
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,XS))) -> mark(XS)
            active(zeros()) -> mark(cons(0(),zeros()))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(tail(X)) -> tail(proper(X))
            proper(zeros()) -> ok(zeros())
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok
            ,zeros}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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