* Step 1: Sum WORST_CASE(Omega(n^1),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(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(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            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,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,top} and constructors {0
            ,mark,nil,ok,tt,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(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(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(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            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,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,top} and constructors {0
            ,mark,nil,ok,tt,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          and(x,y){x -> mark(x)} =
            and(mark(x),y) ->^+ mark(and(x,y))
              = C[and(x,y) = and(x,y){}]

** Step 1.b: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(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(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            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,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,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() -> 15
          0_2() -> 24
          0_3() -> 35
          active_0(1) -> 2
          active_0(6) -> 2
          active_0(7) -> 2
          active_0(8) -> 2
          active_0(12) -> 2
          active_0(13) -> 2
          active_1(1) -> 21
          active_1(6) -> 21
          active_1(7) -> 21
          active_1(8) -> 21
          active_1(12) -> 21
          active_1(13) -> 21
          active_2(15) -> 22
          active_2(16) -> 22
          active_3(30) -> 29
          active_4(24) -> 34
          active_4(28) -> 34
          active_4(36) -> 37
          active_5(35) -> 38
          and_0(1,1) -> 3
          and_0(1,6) -> 3
          and_0(1,7) -> 3
          and_0(1,8) -> 3
          and_0(1,12) -> 3
          and_0(1,13) -> 3
          and_0(6,1) -> 3
          and_0(6,6) -> 3
          and_0(6,7) -> 3
          and_0(6,8) -> 3
          and_0(6,12) -> 3
          and_0(6,13) -> 3
          and_0(7,1) -> 3
          and_0(7,6) -> 3
          and_0(7,7) -> 3
          and_0(7,8) -> 3
          and_0(7,12) -> 3
          and_0(7,13) -> 3
          and_0(8,1) -> 3
          and_0(8,6) -> 3
          and_0(8,7) -> 3
          and_0(8,8) -> 3
          and_0(8,12) -> 3
          and_0(8,13) -> 3
          and_0(12,1) -> 3
          and_0(12,6) -> 3
          and_0(12,7) -> 3
          and_0(12,8) -> 3
          and_0(12,12) -> 3
          and_0(12,13) -> 3
          and_0(13,1) -> 3
          and_0(13,6) -> 3
          and_0(13,7) -> 3
          and_0(13,8) -> 3
          and_0(13,12) -> 3
          and_0(13,13) -> 3
          and_1(1,1) -> 17
          and_1(1,6) -> 17
          and_1(1,7) -> 17
          and_1(1,8) -> 17
          and_1(1,12) -> 17
          and_1(1,13) -> 17
          and_1(6,1) -> 17
          and_1(6,6) -> 17
          and_1(6,7) -> 17
          and_1(6,8) -> 17
          and_1(6,12) -> 17
          and_1(6,13) -> 17
          and_1(7,1) -> 17
          and_1(7,6) -> 17
          and_1(7,7) -> 17
          and_1(7,8) -> 17
          and_1(7,12) -> 17
          and_1(7,13) -> 17
          and_1(8,1) -> 17
          and_1(8,6) -> 17
          and_1(8,7) -> 17
          and_1(8,8) -> 17
          and_1(8,12) -> 17
          and_1(8,13) -> 17
          and_1(12,1) -> 17
          and_1(12,6) -> 17
          and_1(12,7) -> 17
          and_1(12,8) -> 17
          and_1(12,12) -> 17
          and_1(12,13) -> 17
          and_1(13,1) -> 17
          and_1(13,6) -> 17
          and_1(13,7) -> 17
          and_1(13,8) -> 17
          and_1(13,12) -> 17
          and_1(13,13) -> 17
          cons_0(1,1) -> 4
          cons_0(1,6) -> 4
          cons_0(1,7) -> 4
          cons_0(1,8) -> 4
          cons_0(1,12) -> 4
          cons_0(1,13) -> 4
          cons_0(6,1) -> 4
          cons_0(6,6) -> 4
          cons_0(6,7) -> 4
          cons_0(6,8) -> 4
          cons_0(6,12) -> 4
          cons_0(6,13) -> 4
          cons_0(7,1) -> 4
          cons_0(7,6) -> 4
          cons_0(7,7) -> 4
          cons_0(7,8) -> 4
          cons_0(7,12) -> 4
          cons_0(7,13) -> 4
          cons_0(8,1) -> 4
          cons_0(8,6) -> 4
          cons_0(8,7) -> 4
          cons_0(8,8) -> 4
          cons_0(8,12) -> 4
          cons_0(8,13) -> 4
          cons_0(12,1) -> 4
          cons_0(12,6) -> 4
          cons_0(12,7) -> 4
          cons_0(12,8) -> 4
          cons_0(12,12) -> 4
          cons_0(12,13) -> 4
          cons_0(13,1) -> 4
          cons_0(13,6) -> 4
          cons_0(13,7) -> 4
          cons_0(13,8) -> 4
          cons_0(13,12) -> 4
          cons_0(13,13) -> 4
          cons_1(1,1) -> 18
          cons_1(1,6) -> 18
          cons_1(1,7) -> 18
          cons_1(1,8) -> 18
          cons_1(1,12) -> 18
          cons_1(1,13) -> 18
          cons_1(6,1) -> 18
          cons_1(6,6) -> 18
          cons_1(6,7) -> 18
          cons_1(6,8) -> 18
          cons_1(6,12) -> 18
          cons_1(6,13) -> 18
          cons_1(7,1) -> 18
          cons_1(7,6) -> 18
          cons_1(7,7) -> 18
          cons_1(7,8) -> 18
          cons_1(7,12) -> 18
          cons_1(7,13) -> 18
          cons_1(8,1) -> 18
          cons_1(8,6) -> 18
          cons_1(8,7) -> 18
          cons_1(8,8) -> 18
          cons_1(8,12) -> 18
          cons_1(8,13) -> 18
          cons_1(12,1) -> 18
          cons_1(12,6) -> 18
          cons_1(12,7) -> 18
          cons_1(12,8) -> 18
          cons_1(12,12) -> 18
          cons_1(12,13) -> 18
          cons_1(13,1) -> 18
          cons_1(13,6) -> 18
          cons_1(13,7) -> 18
          cons_1(13,8) -> 18
          cons_1(13,12) -> 18
          cons_1(13,13) -> 18
          cons_1(15,16) -> 14
          cons_2(24,25) -> 23
          cons_2(26,27) -> 22
          cons_3(24,25) -> 30
          cons_3(28,25) -> 30
          cons_3(31,32) -> 29
          cons_4(34,25) -> 29
          cons_4(35,33) -> 36
          cons_5(38,33) -> 37
          length_0(1) -> 5
          length_0(6) -> 5
          length_0(7) -> 5
          length_0(8) -> 5
          length_0(12) -> 5
          length_0(13) -> 5
          length_1(1) -> 19
          length_1(6) -> 19
          length_1(7) -> 19
          length_1(8) -> 19
          length_1(12) -> 19
          length_1(13) -> 19
          mark_0(1) -> 6
          mark_0(6) -> 6
          mark_0(7) -> 6
          mark_0(8) -> 6
          mark_0(12) -> 6
          mark_0(13) -> 6
          mark_1(14) -> 2
          mark_1(14) -> 21
          mark_1(17) -> 3
          mark_1(17) -> 17
          mark_1(18) -> 4
          mark_1(18) -> 18
          mark_1(19) -> 5
          mark_1(19) -> 19
          mark_1(20) -> 10
          mark_1(20) -> 20
          mark_2(23) -> 22
          nil_0() -> 7
          nil_1() -> 15
          nil_2() -> 28
          ok_0(1) -> 8
          ok_0(6) -> 8
          ok_0(7) -> 8
          ok_0(8) -> 8
          ok_0(12) -> 8
          ok_0(13) -> 8
          ok_1(15) -> 9
          ok_1(15) -> 21
          ok_1(16) -> 9
          ok_1(16) -> 21
          ok_1(17) -> 3
          ok_1(17) -> 17
          ok_1(18) -> 4
          ok_1(18) -> 18
          ok_1(19) -> 5
          ok_1(19) -> 19
          ok_1(20) -> 10
          ok_1(20) -> 20
          ok_2(24) -> 26
          ok_2(25) -> 27
          ok_2(28) -> 26
          ok_3(30) -> 22
          ok_3(33) -> 32
          ok_3(35) -> 31
          ok_4(36) -> 29
          proper_0(1) -> 9
          proper_0(6) -> 9
          proper_0(7) -> 9
          proper_0(8) -> 9
          proper_0(12) -> 9
          proper_0(13) -> 9
          proper_1(1) -> 21
          proper_1(6) -> 21
          proper_1(7) -> 21
          proper_1(8) -> 21
          proper_1(12) -> 21
          proper_1(13) -> 21
          proper_2(14) -> 22
          proper_2(15) -> 26
          proper_2(16) -> 27
          proper_3(23) -> 29
          proper_3(24) -> 31
          proper_3(25) -> 32
          s_0(1) -> 10
          s_0(6) -> 10
          s_0(7) -> 10
          s_0(8) -> 10
          s_0(12) -> 10
          s_0(13) -> 10
          s_1(1) -> 20
          s_1(6) -> 20
          s_1(7) -> 20
          s_1(8) -> 20
          s_1(12) -> 20
          s_1(13) -> 20
          top_0(1) -> 11
          top_0(6) -> 11
          top_0(7) -> 11
          top_0(8) -> 11
          top_0(12) -> 11
          top_0(13) -> 11
          top_1(21) -> 11
          top_2(22) -> 11
          top_3(29) -> 11
          top_4(37) -> 11
          tt_0() -> 12
          tt_1() -> 15
          tt_2() -> 28
          zeros_0() -> 13
          zeros_1() -> 16
          zeros_2() -> 25
          zeros_3() -> 33
** Step 1.b: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(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(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            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,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,length,proper,s,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(Omega(n^1),O(n^1))