* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(U12(tt(),L))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),L)) -> mark(s(length(L)))
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(tt(),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(zeros()) -> mark(cons(0(),zeros()))
            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(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U12(X1,X2)) -> U12(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:
            {U11/2,U12/2,active/1,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 {U11,U12,active,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:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(U12(tt(),L))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),L)) -> mark(s(length(L)))
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(tt(),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(zeros()) -> mark(cons(0(),zeros()))
            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(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U12(X1,X2)) -> U12(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:
            {U11/2,U12/2,active/1,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 {U11,U12,active,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:
          U11(x,y){x -> mark(x)} =
            U11(mark(x),y) ->^+ mark(U11(x,y))
              = C[U11(x,y) = U11(x,y){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(U12(tt(),L))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),L)) -> mark(s(length(L)))
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(tt(),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(zeros()) -> mark(cons(0(),zeros()))
            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(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U12(X1,X2)) -> U12(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:
            {U11/2,U12/2,active/1,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 {U11,U12,active,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() -> 18
          0_2() -> 26
          0_3() -> 37
          U11_0(1,1) -> 2
          U11_0(1,7) -> 2
          U11_0(1,8) -> 2
          U11_0(1,9) -> 2
          U11_0(1,13) -> 2
          U11_0(1,14) -> 2
          U11_0(7,1) -> 2
          U11_0(7,7) -> 2
          U11_0(7,8) -> 2
          U11_0(7,9) -> 2
          U11_0(7,13) -> 2
          U11_0(7,14) -> 2
          U11_0(8,1) -> 2
          U11_0(8,7) -> 2
          U11_0(8,8) -> 2
          U11_0(8,9) -> 2
          U11_0(8,13) -> 2
          U11_0(8,14) -> 2
          U11_0(9,1) -> 2
          U11_0(9,7) -> 2
          U11_0(9,8) -> 2
          U11_0(9,9) -> 2
          U11_0(9,13) -> 2
          U11_0(9,14) -> 2
          U11_0(13,1) -> 2
          U11_0(13,7) -> 2
          U11_0(13,8) -> 2
          U11_0(13,9) -> 2
          U11_0(13,13) -> 2
          U11_0(13,14) -> 2
          U11_0(14,1) -> 2
          U11_0(14,7) -> 2
          U11_0(14,8) -> 2
          U11_0(14,9) -> 2
          U11_0(14,13) -> 2
          U11_0(14,14) -> 2
          U11_1(1,1) -> 15
          U11_1(1,7) -> 15
          U11_1(1,8) -> 15
          U11_1(1,9) -> 15
          U11_1(1,13) -> 15
          U11_1(1,14) -> 15
          U11_1(7,1) -> 15
          U11_1(7,7) -> 15
          U11_1(7,8) -> 15
          U11_1(7,9) -> 15
          U11_1(7,13) -> 15
          U11_1(7,14) -> 15
          U11_1(8,1) -> 15
          U11_1(8,7) -> 15
          U11_1(8,8) -> 15
          U11_1(8,9) -> 15
          U11_1(8,13) -> 15
          U11_1(8,14) -> 15
          U11_1(9,1) -> 15
          U11_1(9,7) -> 15
          U11_1(9,8) -> 15
          U11_1(9,9) -> 15
          U11_1(9,13) -> 15
          U11_1(9,14) -> 15
          U11_1(13,1) -> 15
          U11_1(13,7) -> 15
          U11_1(13,8) -> 15
          U11_1(13,9) -> 15
          U11_1(13,13) -> 15
          U11_1(13,14) -> 15
          U11_1(14,1) -> 15
          U11_1(14,7) -> 15
          U11_1(14,8) -> 15
          U11_1(14,9) -> 15
          U11_1(14,13) -> 15
          U11_1(14,14) -> 15
          U12_0(1,1) -> 3
          U12_0(1,7) -> 3
          U12_0(1,8) -> 3
          U12_0(1,9) -> 3
          U12_0(1,13) -> 3
          U12_0(1,14) -> 3
          U12_0(7,1) -> 3
          U12_0(7,7) -> 3
          U12_0(7,8) -> 3
          U12_0(7,9) -> 3
          U12_0(7,13) -> 3
          U12_0(7,14) -> 3
          U12_0(8,1) -> 3
          U12_0(8,7) -> 3
          U12_0(8,8) -> 3
          U12_0(8,9) -> 3
          U12_0(8,13) -> 3
          U12_0(8,14) -> 3
          U12_0(9,1) -> 3
          U12_0(9,7) -> 3
          U12_0(9,8) -> 3
          U12_0(9,9) -> 3
          U12_0(9,13) -> 3
          U12_0(9,14) -> 3
          U12_0(13,1) -> 3
          U12_0(13,7) -> 3
          U12_0(13,8) -> 3
          U12_0(13,9) -> 3
          U12_0(13,13) -> 3
          U12_0(13,14) -> 3
          U12_0(14,1) -> 3
          U12_0(14,7) -> 3
          U12_0(14,8) -> 3
          U12_0(14,9) -> 3
          U12_0(14,13) -> 3
          U12_0(14,14) -> 3
          U12_1(1,1) -> 16
          U12_1(1,7) -> 16
          U12_1(1,8) -> 16
          U12_1(1,9) -> 16
          U12_1(1,13) -> 16
          U12_1(1,14) -> 16
          U12_1(7,1) -> 16
          U12_1(7,7) -> 16
          U12_1(7,8) -> 16
          U12_1(7,9) -> 16
          U12_1(7,13) -> 16
          U12_1(7,14) -> 16
          U12_1(8,1) -> 16
          U12_1(8,7) -> 16
          U12_1(8,8) -> 16
          U12_1(8,9) -> 16
          U12_1(8,13) -> 16
          U12_1(8,14) -> 16
          U12_1(9,1) -> 16
          U12_1(9,7) -> 16
          U12_1(9,8) -> 16
          U12_1(9,9) -> 16
          U12_1(9,13) -> 16
          U12_1(9,14) -> 16
          U12_1(13,1) -> 16
          U12_1(13,7) -> 16
          U12_1(13,8) -> 16
          U12_1(13,9) -> 16
          U12_1(13,13) -> 16
          U12_1(13,14) -> 16
          U12_1(14,1) -> 16
          U12_1(14,7) -> 16
          U12_1(14,8) -> 16
          U12_1(14,9) -> 16
          U12_1(14,13) -> 16
          U12_1(14,14) -> 16
          active_0(1) -> 4
          active_0(7) -> 4
          active_0(8) -> 4
          active_0(9) -> 4
          active_0(13) -> 4
          active_0(14) -> 4
          active_1(1) -> 23
          active_1(7) -> 23
          active_1(8) -> 23
          active_1(9) -> 23
          active_1(13) -> 23
          active_1(14) -> 23
          active_2(18) -> 24
          active_2(19) -> 24
          active_3(32) -> 31
          active_4(26) -> 36
          active_4(30) -> 36
          active_4(38) -> 39
          active_5(37) -> 40
          cons_0(1,1) -> 5
          cons_0(1,7) -> 5
          cons_0(1,8) -> 5
          cons_0(1,9) -> 5
          cons_0(1,13) -> 5
          cons_0(1,14) -> 5
          cons_0(7,1) -> 5
          cons_0(7,7) -> 5
          cons_0(7,8) -> 5
          cons_0(7,9) -> 5
          cons_0(7,13) -> 5
          cons_0(7,14) -> 5
          cons_0(8,1) -> 5
          cons_0(8,7) -> 5
          cons_0(8,8) -> 5
          cons_0(8,9) -> 5
          cons_0(8,13) -> 5
          cons_0(8,14) -> 5
          cons_0(9,1) -> 5
          cons_0(9,7) -> 5
          cons_0(9,8) -> 5
          cons_0(9,9) -> 5
          cons_0(9,13) -> 5
          cons_0(9,14) -> 5
          cons_0(13,1) -> 5
          cons_0(13,7) -> 5
          cons_0(13,8) -> 5
          cons_0(13,9) -> 5
          cons_0(13,13) -> 5
          cons_0(13,14) -> 5
          cons_0(14,1) -> 5
          cons_0(14,7) -> 5
          cons_0(14,8) -> 5
          cons_0(14,9) -> 5
          cons_0(14,13) -> 5
          cons_0(14,14) -> 5
          cons_1(1,1) -> 20
          cons_1(1,7) -> 20
          cons_1(1,8) -> 20
          cons_1(1,9) -> 20
          cons_1(1,13) -> 20
          cons_1(1,14) -> 20
          cons_1(7,1) -> 20
          cons_1(7,7) -> 20
          cons_1(7,8) -> 20
          cons_1(7,9) -> 20
          cons_1(7,13) -> 20
          cons_1(7,14) -> 20
          cons_1(8,1) -> 20
          cons_1(8,7) -> 20
          cons_1(8,8) -> 20
          cons_1(8,9) -> 20
          cons_1(8,13) -> 20
          cons_1(8,14) -> 20
          cons_1(9,1) -> 20
          cons_1(9,7) -> 20
          cons_1(9,8) -> 20
          cons_1(9,9) -> 20
          cons_1(9,13) -> 20
          cons_1(9,14) -> 20
          cons_1(13,1) -> 20
          cons_1(13,7) -> 20
          cons_1(13,8) -> 20
          cons_1(13,9) -> 20
          cons_1(13,13) -> 20
          cons_1(13,14) -> 20
          cons_1(14,1) -> 20
          cons_1(14,7) -> 20
          cons_1(14,8) -> 20
          cons_1(14,9) -> 20
          cons_1(14,13) -> 20
          cons_1(14,14) -> 20
          cons_1(18,19) -> 17
          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) -> 6
          length_0(7) -> 6
          length_0(8) -> 6
          length_0(9) -> 6
          length_0(13) -> 6
          length_0(14) -> 6
          length_1(1) -> 21
          length_1(7) -> 21
          length_1(8) -> 21
          length_1(9) -> 21
          length_1(13) -> 21
          length_1(14) -> 21
          mark_0(1) -> 7
          mark_0(7) -> 7
          mark_0(8) -> 7
          mark_0(9) -> 7
          mark_0(13) -> 7
          mark_0(14) -> 7
          mark_1(15) -> 2
          mark_1(15) -> 15
          mark_1(16) -> 3
          mark_1(16) -> 16
          mark_1(17) -> 4
          mark_1(17) -> 23
          mark_1(20) -> 5
          mark_1(20) -> 20
          mark_1(21) -> 6
          mark_1(21) -> 21
          mark_1(22) -> 11
          mark_1(22) -> 22
          mark_2(25) -> 24
          nil_0() -> 8
          nil_1() -> 18
          nil_2() -> 30
          ok_0(1) -> 9
          ok_0(7) -> 9
          ok_0(8) -> 9
          ok_0(9) -> 9
          ok_0(13) -> 9
          ok_0(14) -> 9
          ok_1(15) -> 2
          ok_1(15) -> 15
          ok_1(16) -> 3
          ok_1(16) -> 16
          ok_1(18) -> 10
          ok_1(18) -> 23
          ok_1(19) -> 10
          ok_1(19) -> 23
          ok_1(20) -> 5
          ok_1(20) -> 20
          ok_1(21) -> 6
          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) -> 10
          proper_0(7) -> 10
          proper_0(8) -> 10
          proper_0(9) -> 10
          proper_0(13) -> 10
          proper_0(14) -> 10
          proper_1(1) -> 23
          proper_1(7) -> 23
          proper_1(8) -> 23
          proper_1(9) -> 23
          proper_1(13) -> 23
          proper_1(14) -> 23
          proper_2(17) -> 24
          proper_2(18) -> 28
          proper_2(19) -> 29
          proper_3(25) -> 31
          proper_3(26) -> 33
          proper_3(27) -> 34
          s_0(1) -> 11
          s_0(7) -> 11
          s_0(8) -> 11
          s_0(9) -> 11
          s_0(13) -> 11
          s_0(14) -> 11
          s_1(1) -> 22
          s_1(7) -> 22
          s_1(8) -> 22
          s_1(9) -> 22
          s_1(13) -> 22
          s_1(14) -> 22
          top_0(1) -> 12
          top_0(7) -> 12
          top_0(8) -> 12
          top_0(9) -> 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() -> 18
          tt_2() -> 30
          zeros_0() -> 14
          zeros_1() -> 19
          zeros_2() -> 27
          zeros_3() -> 35
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(U12(tt(),L))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),L)) -> mark(s(length(L)))
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(tt(),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(zeros()) -> mark(cons(0(),zeros()))
            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(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U12(X1,X2)) -> U12(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:
            {U11/2,U12/2,active/1,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 {U11,U12,active,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))