* Step 1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(s(length(L)))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            active(take(0(),IL)) -> mark(nil())
            active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
            active(zeros()) -> mark(cons(0(),zeros()))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            length(mark(X)) -> mark(length(X))
            length(ok(X)) -> ok(length(X))
            proper(0()) -> ok(0())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(length(X)) -> length(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            take(X1,mark(X2)) -> mark(take(X1,X2))
            take(mark(X1),X2) -> mark(take(X1,X2))
            take(ok(X1),ok(X2)) -> ok(take(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark
            ,nil,ok,tt,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() -> 16
          0_2() -> 26
          0_3() -> 37
          active_0(1) -> 2
          active_0(6) -> 2
          active_0(7) -> 2
          active_0(8) -> 2
          active_0(13) -> 2
          active_0(14) -> 2
          active_1(1) -> 23
          active_1(6) -> 23
          active_1(7) -> 23
          active_1(8) -> 23
          active_1(13) -> 23
          active_1(14) -> 23
          active_2(16) -> 24
          active_2(17) -> 24
          active_3(32) -> 31
          active_4(26) -> 36
          active_4(30) -> 36
          active_4(38) -> 39
          active_5(37) -> 40
          and_0(1,1) -> 3
          and_0(1,6) -> 3
          and_0(1,7) -> 3
          and_0(1,8) -> 3
          and_0(1,13) -> 3
          and_0(1,14) -> 3
          and_0(6,1) -> 3
          and_0(6,6) -> 3
          and_0(6,7) -> 3
          and_0(6,8) -> 3
          and_0(6,13) -> 3
          and_0(6,14) -> 3
          and_0(7,1) -> 3
          and_0(7,6) -> 3
          and_0(7,7) -> 3
          and_0(7,8) -> 3
          and_0(7,13) -> 3
          and_0(7,14) -> 3
          and_0(8,1) -> 3
          and_0(8,6) -> 3
          and_0(8,7) -> 3
          and_0(8,8) -> 3
          and_0(8,13) -> 3
          and_0(8,14) -> 3
          and_0(13,1) -> 3
          and_0(13,6) -> 3
          and_0(13,7) -> 3
          and_0(13,8) -> 3
          and_0(13,13) -> 3
          and_0(13,14) -> 3
          and_0(14,1) -> 3
          and_0(14,6) -> 3
          and_0(14,7) -> 3
          and_0(14,8) -> 3
          and_0(14,13) -> 3
          and_0(14,14) -> 3
          and_1(1,1) -> 18
          and_1(1,6) -> 18
          and_1(1,7) -> 18
          and_1(1,8) -> 18
          and_1(1,13) -> 18
          and_1(1,14) -> 18
          and_1(6,1) -> 18
          and_1(6,6) -> 18
          and_1(6,7) -> 18
          and_1(6,8) -> 18
          and_1(6,13) -> 18
          and_1(6,14) -> 18
          and_1(7,1) -> 18
          and_1(7,6) -> 18
          and_1(7,7) -> 18
          and_1(7,8) -> 18
          and_1(7,13) -> 18
          and_1(7,14) -> 18
          and_1(8,1) -> 18
          and_1(8,6) -> 18
          and_1(8,7) -> 18
          and_1(8,8) -> 18
          and_1(8,13) -> 18
          and_1(8,14) -> 18
          and_1(13,1) -> 18
          and_1(13,6) -> 18
          and_1(13,7) -> 18
          and_1(13,8) -> 18
          and_1(13,13) -> 18
          and_1(13,14) -> 18
          and_1(14,1) -> 18
          and_1(14,6) -> 18
          and_1(14,7) -> 18
          and_1(14,8) -> 18
          and_1(14,13) -> 18
          and_1(14,14) -> 18
          cons_0(1,1) -> 4
          cons_0(1,6) -> 4
          cons_0(1,7) -> 4
          cons_0(1,8) -> 4
          cons_0(1,13) -> 4
          cons_0(1,14) -> 4
          cons_0(6,1) -> 4
          cons_0(6,6) -> 4
          cons_0(6,7) -> 4
          cons_0(6,8) -> 4
          cons_0(6,13) -> 4
          cons_0(6,14) -> 4
          cons_0(7,1) -> 4
          cons_0(7,6) -> 4
          cons_0(7,7) -> 4
          cons_0(7,8) -> 4
          cons_0(7,13) -> 4
          cons_0(7,14) -> 4
          cons_0(8,1) -> 4
          cons_0(8,6) -> 4
          cons_0(8,7) -> 4
          cons_0(8,8) -> 4
          cons_0(8,13) -> 4
          cons_0(8,14) -> 4
          cons_0(13,1) -> 4
          cons_0(13,6) -> 4
          cons_0(13,7) -> 4
          cons_0(13,8) -> 4
          cons_0(13,13) -> 4
          cons_0(13,14) -> 4
          cons_0(14,1) -> 4
          cons_0(14,6) -> 4
          cons_0(14,7) -> 4
          cons_0(14,8) -> 4
          cons_0(14,13) -> 4
          cons_0(14,14) -> 4
          cons_1(1,1) -> 19
          cons_1(1,6) -> 19
          cons_1(1,7) -> 19
          cons_1(1,8) -> 19
          cons_1(1,13) -> 19
          cons_1(1,14) -> 19
          cons_1(6,1) -> 19
          cons_1(6,6) -> 19
          cons_1(6,7) -> 19
          cons_1(6,8) -> 19
          cons_1(6,13) -> 19
          cons_1(6,14) -> 19
          cons_1(7,1) -> 19
          cons_1(7,6) -> 19
          cons_1(7,7) -> 19
          cons_1(7,8) -> 19
          cons_1(7,13) -> 19
          cons_1(7,14) -> 19
          cons_1(8,1) -> 19
          cons_1(8,6) -> 19
          cons_1(8,7) -> 19
          cons_1(8,8) -> 19
          cons_1(8,13) -> 19
          cons_1(8,14) -> 19
          cons_1(13,1) -> 19
          cons_1(13,6) -> 19
          cons_1(13,7) -> 19
          cons_1(13,8) -> 19
          cons_1(13,13) -> 19
          cons_1(13,14) -> 19
          cons_1(14,1) -> 19
          cons_1(14,6) -> 19
          cons_1(14,7) -> 19
          cons_1(14,8) -> 19
          cons_1(14,13) -> 19
          cons_1(14,14) -> 19
          cons_1(16,17) -> 15
          cons_2(26,27) -> 25
          cons_2(28,29) -> 24
          cons_3(26,27) -> 32
          cons_3(30,27) -> 32
          cons_3(33,34) -> 31
          cons_4(36,27) -> 31
          cons_4(37,35) -> 38
          cons_5(40,35) -> 39
          length_0(1) -> 5
          length_0(6) -> 5
          length_0(7) -> 5
          length_0(8) -> 5
          length_0(13) -> 5
          length_0(14) -> 5
          length_1(1) -> 20
          length_1(6) -> 20
          length_1(7) -> 20
          length_1(8) -> 20
          length_1(13) -> 20
          length_1(14) -> 20
          mark_0(1) -> 6
          mark_0(6) -> 6
          mark_0(7) -> 6
          mark_0(8) -> 6
          mark_0(13) -> 6
          mark_0(14) -> 6
          mark_1(15) -> 2
          mark_1(15) -> 23
          mark_1(18) -> 3
          mark_1(18) -> 18
          mark_1(19) -> 4
          mark_1(19) -> 19
          mark_1(20) -> 5
          mark_1(20) -> 20
          mark_1(21) -> 10
          mark_1(21) -> 21
          mark_1(22) -> 11
          mark_1(22) -> 22
          mark_2(25) -> 24
          nil_0() -> 7
          nil_1() -> 16
          nil_2() -> 30
          ok_0(1) -> 8
          ok_0(6) -> 8
          ok_0(7) -> 8
          ok_0(8) -> 8
          ok_0(13) -> 8
          ok_0(14) -> 8
          ok_1(16) -> 9
          ok_1(16) -> 23
          ok_1(17) -> 9
          ok_1(17) -> 23
          ok_1(18) -> 3
          ok_1(18) -> 18
          ok_1(19) -> 4
          ok_1(19) -> 19
          ok_1(20) -> 5
          ok_1(20) -> 20
          ok_1(21) -> 10
          ok_1(21) -> 21
          ok_1(22) -> 11
          ok_1(22) -> 22
          ok_2(26) -> 28
          ok_2(27) -> 29
          ok_2(30) -> 28
          ok_3(32) -> 24
          ok_3(35) -> 34
          ok_3(37) -> 33
          ok_4(38) -> 31
          proper_0(1) -> 9
          proper_0(6) -> 9
          proper_0(7) -> 9
          proper_0(8) -> 9
          proper_0(13) -> 9
          proper_0(14) -> 9
          proper_1(1) -> 23
          proper_1(6) -> 23
          proper_1(7) -> 23
          proper_1(8) -> 23
          proper_1(13) -> 23
          proper_1(14) -> 23
          proper_2(15) -> 24
          proper_2(16) -> 28
          proper_2(17) -> 29
          proper_3(25) -> 31
          proper_3(26) -> 33
          proper_3(27) -> 34
          s_0(1) -> 10
          s_0(6) -> 10
          s_0(7) -> 10
          s_0(8) -> 10
          s_0(13) -> 10
          s_0(14) -> 10
          s_1(1) -> 21
          s_1(6) -> 21
          s_1(7) -> 21
          s_1(8) -> 21
          s_1(13) -> 21
          s_1(14) -> 21
          take_0(1,1) -> 11
          take_0(1,6) -> 11
          take_0(1,7) -> 11
          take_0(1,8) -> 11
          take_0(1,13) -> 11
          take_0(1,14) -> 11
          take_0(6,1) -> 11
          take_0(6,6) -> 11
          take_0(6,7) -> 11
          take_0(6,8) -> 11
          take_0(6,13) -> 11
          take_0(6,14) -> 11
          take_0(7,1) -> 11
          take_0(7,6) -> 11
          take_0(7,7) -> 11
          take_0(7,8) -> 11
          take_0(7,13) -> 11
          take_0(7,14) -> 11
          take_0(8,1) -> 11
          take_0(8,6) -> 11
          take_0(8,7) -> 11
          take_0(8,8) -> 11
          take_0(8,13) -> 11
          take_0(8,14) -> 11
          take_0(13,1) -> 11
          take_0(13,6) -> 11
          take_0(13,7) -> 11
          take_0(13,8) -> 11
          take_0(13,13) -> 11
          take_0(13,14) -> 11
          take_0(14,1) -> 11
          take_0(14,6) -> 11
          take_0(14,7) -> 11
          take_0(14,8) -> 11
          take_0(14,13) -> 11
          take_0(14,14) -> 11
          take_1(1,1) -> 22
          take_1(1,6) -> 22
          take_1(1,7) -> 22
          take_1(1,8) -> 22
          take_1(1,13) -> 22
          take_1(1,14) -> 22
          take_1(6,1) -> 22
          take_1(6,6) -> 22
          take_1(6,7) -> 22
          take_1(6,8) -> 22
          take_1(6,13) -> 22
          take_1(6,14) -> 22
          take_1(7,1) -> 22
          take_1(7,6) -> 22
          take_1(7,7) -> 22
          take_1(7,8) -> 22
          take_1(7,13) -> 22
          take_1(7,14) -> 22
          take_1(8,1) -> 22
          take_1(8,6) -> 22
          take_1(8,7) -> 22
          take_1(8,8) -> 22
          take_1(8,13) -> 22
          take_1(8,14) -> 22
          take_1(13,1) -> 22
          take_1(13,6) -> 22
          take_1(13,7) -> 22
          take_1(13,8) -> 22
          take_1(13,13) -> 22
          take_1(13,14) -> 22
          take_1(14,1) -> 22
          take_1(14,6) -> 22
          take_1(14,7) -> 22
          take_1(14,8) -> 22
          take_1(14,13) -> 22
          take_1(14,14) -> 22
          top_0(1) -> 12
          top_0(6) -> 12
          top_0(7) -> 12
          top_0(8) -> 12
          top_0(13) -> 12
          top_0(14) -> 12
          top_1(23) -> 12
          top_2(24) -> 12
          top_3(31) -> 12
          top_4(39) -> 12
          tt_0() -> 13
          tt_1() -> 16
          tt_2() -> 30
          zeros_0() -> 14
          zeros_1() -> 17
          zeros_2() -> 27
          zeros_3() -> 35
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(s(length(L)))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            active(take(0(),IL)) -> mark(nil())
            active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
            active(zeros()) -> mark(cons(0(),zeros()))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            length(mark(X)) -> mark(length(X))
            length(ok(X)) -> ok(length(X))
            proper(0()) -> ok(0())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(length(X)) -> length(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            take(X1,mark(X2)) -> mark(take(X1,X2))
            take(mark(X1),X2) -> mark(take(X1,X2))
            take(ok(X1),ok(X2)) -> ok(take(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,and/2,cons/2,length/1,proper/1,s/1,take/2,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,take,top} and constructors {0,mark
            ,nil,ok,tt,zeros}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))