* Step 1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            __(X1,mark(X2)) -> mark(__(X1,X2))
            __(mark(X1),X2) -> mark(__(X1,X2))
            __(ok(X1),ok(X2)) -> ok(__(X1,X2))
            active(__(X,nil())) -> mark(X)
            active(__(X1,X2)) -> __(X1,active(X2))
            active(__(X1,X2)) -> __(active(X1),X2)
            active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
            active(__(nil(),X)) -> mark(X)
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(isList(V)) -> mark(isNeList(V))
            active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2)))
            active(isList(nil())) -> mark(tt())
            active(isNeList(V)) -> mark(isQid(V))
            active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2)))
            active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2)))
            active(isNePal(V)) -> mark(isQid(V))
            active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P)))
            active(isPal(V)) -> mark(isNePal(V))
            active(isPal(nil())) -> mark(tt())
            active(isQid(a())) -> mark(tt())
            active(isQid(e())) -> mark(tt())
            active(isQid(i())) -> mark(tt())
            active(isQid(o())) -> mark(tt())
            active(isQid(u())) -> mark(tt())
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            isList(ok(X)) -> ok(isList(X))
            isNeList(ok(X)) -> ok(isNeList(X))
            isNePal(ok(X)) -> ok(isNePal(X))
            isPal(ok(X)) -> ok(isPal(X))
            isQid(ok(X)) -> ok(isQid(X))
            proper(__(X1,X2)) -> __(proper(X1),proper(X2))
            proper(a()) -> ok(a())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(e()) -> ok(e())
            proper(i()) -> ok(i())
            proper(isList(X)) -> isList(proper(X))
            proper(isNeList(X)) -> isNeList(proper(X))
            proper(isNePal(X)) -> isNePal(proper(X))
            proper(isPal(X)) -> isPal(proper(X))
            proper(isQid(X)) -> isQid(proper(X))
            proper(nil()) -> ok(nil())
            proper(o()) -> ok(o())
            proper(tt()) -> ok(tt())
            proper(u()) -> ok(u())
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1
            ,nil/0,o/0,ok/1,tt/0,u/0}
        - Obligation:
             runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper
            ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          ___0(2,2) -> 1
          ___0(2,5) -> 1
          ___0(2,6) -> 1
          ___0(2,12) -> 1
          ___0(2,13) -> 1
          ___0(2,14) -> 1
          ___0(2,15) -> 1
          ___0(2,18) -> 1
          ___0(2,19) -> 1
          ___0(5,2) -> 1
          ___0(5,5) -> 1
          ___0(5,6) -> 1
          ___0(5,12) -> 1
          ___0(5,13) -> 1
          ___0(5,14) -> 1
          ___0(5,15) -> 1
          ___0(5,18) -> 1
          ___0(5,19) -> 1
          ___0(6,2) -> 1
          ___0(6,5) -> 1
          ___0(6,6) -> 1
          ___0(6,12) -> 1
          ___0(6,13) -> 1
          ___0(6,14) -> 1
          ___0(6,15) -> 1
          ___0(6,18) -> 1
          ___0(6,19) -> 1
          ___0(12,2) -> 1
          ___0(12,5) -> 1
          ___0(12,6) -> 1
          ___0(12,12) -> 1
          ___0(12,13) -> 1
          ___0(12,14) -> 1
          ___0(12,15) -> 1
          ___0(12,18) -> 1
          ___0(12,19) -> 1
          ___0(13,2) -> 1
          ___0(13,5) -> 1
          ___0(13,6) -> 1
          ___0(13,12) -> 1
          ___0(13,13) -> 1
          ___0(13,14) -> 1
          ___0(13,15) -> 1
          ___0(13,18) -> 1
          ___0(13,19) -> 1
          ___0(14,2) -> 1
          ___0(14,5) -> 1
          ___0(14,6) -> 1
          ___0(14,12) -> 1
          ___0(14,13) -> 1
          ___0(14,14) -> 1
          ___0(14,15) -> 1
          ___0(14,18) -> 1
          ___0(14,19) -> 1
          ___0(15,2) -> 1
          ___0(15,5) -> 1
          ___0(15,6) -> 1
          ___0(15,12) -> 1
          ___0(15,13) -> 1
          ___0(15,14) -> 1
          ___0(15,15) -> 1
          ___0(15,18) -> 1
          ___0(15,19) -> 1
          ___0(18,2) -> 1
          ___0(18,5) -> 1
          ___0(18,6) -> 1
          ___0(18,12) -> 1
          ___0(18,13) -> 1
          ___0(18,14) -> 1
          ___0(18,15) -> 1
          ___0(18,18) -> 1
          ___0(18,19) -> 1
          ___0(19,2) -> 1
          ___0(19,5) -> 1
          ___0(19,6) -> 1
          ___0(19,12) -> 1
          ___0(19,13) -> 1
          ___0(19,14) -> 1
          ___0(19,15) -> 1
          ___0(19,18) -> 1
          ___0(19,19) -> 1
          ___1(2,2) -> 20
          ___1(2,5) -> 20
          ___1(2,6) -> 20
          ___1(2,12) -> 20
          ___1(2,13) -> 20
          ___1(2,14) -> 20
          ___1(2,15) -> 20
          ___1(2,18) -> 20
          ___1(2,19) -> 20
          ___1(5,2) -> 20
          ___1(5,5) -> 20
          ___1(5,6) -> 20
          ___1(5,12) -> 20
          ___1(5,13) -> 20
          ___1(5,14) -> 20
          ___1(5,15) -> 20
          ___1(5,18) -> 20
          ___1(5,19) -> 20
          ___1(6,2) -> 20
          ___1(6,5) -> 20
          ___1(6,6) -> 20
          ___1(6,12) -> 20
          ___1(6,13) -> 20
          ___1(6,14) -> 20
          ___1(6,15) -> 20
          ___1(6,18) -> 20
          ___1(6,19) -> 20
          ___1(12,2) -> 20
          ___1(12,5) -> 20
          ___1(12,6) -> 20
          ___1(12,12) -> 20
          ___1(12,13) -> 20
          ___1(12,14) -> 20
          ___1(12,15) -> 20
          ___1(12,18) -> 20
          ___1(12,19) -> 20
          ___1(13,2) -> 20
          ___1(13,5) -> 20
          ___1(13,6) -> 20
          ___1(13,12) -> 20
          ___1(13,13) -> 20
          ___1(13,14) -> 20
          ___1(13,15) -> 20
          ___1(13,18) -> 20
          ___1(13,19) -> 20
          ___1(14,2) -> 20
          ___1(14,5) -> 20
          ___1(14,6) -> 20
          ___1(14,12) -> 20
          ___1(14,13) -> 20
          ___1(14,14) -> 20
          ___1(14,15) -> 20
          ___1(14,18) -> 20
          ___1(14,19) -> 20
          ___1(15,2) -> 20
          ___1(15,5) -> 20
          ___1(15,6) -> 20
          ___1(15,12) -> 20
          ___1(15,13) -> 20
          ___1(15,14) -> 20
          ___1(15,15) -> 20
          ___1(15,18) -> 20
          ___1(15,19) -> 20
          ___1(18,2) -> 20
          ___1(18,5) -> 20
          ___1(18,6) -> 20
          ___1(18,12) -> 20
          ___1(18,13) -> 20
          ___1(18,14) -> 20
          ___1(18,15) -> 20
          ___1(18,18) -> 20
          ___1(18,19) -> 20
          ___1(19,2) -> 20
          ___1(19,5) -> 20
          ___1(19,6) -> 20
          ___1(19,12) -> 20
          ___1(19,13) -> 20
          ___1(19,14) -> 20
          ___1(19,15) -> 20
          ___1(19,18) -> 20
          ___1(19,19) -> 20
          a_0() -> 2
          a_1() -> 27
          active_0(2) -> 3
          active_0(5) -> 3
          active_0(6) -> 3
          active_0(12) -> 3
          active_0(13) -> 3
          active_0(14) -> 3
          active_0(15) -> 3
          active_0(18) -> 3
          active_0(19) -> 3
          active_1(2) -> 28
          active_1(5) -> 28
          active_1(6) -> 28
          active_1(12) -> 28
          active_1(13) -> 28
          active_1(14) -> 28
          active_1(15) -> 28
          active_1(18) -> 28
          active_1(19) -> 28
          active_2(27) -> 29
          and_0(2,2) -> 4
          and_0(2,5) -> 4
          and_0(2,6) -> 4
          and_0(2,12) -> 4
          and_0(2,13) -> 4
          and_0(2,14) -> 4
          and_0(2,15) -> 4
          and_0(2,18) -> 4
          and_0(2,19) -> 4
          and_0(5,2) -> 4
          and_0(5,5) -> 4
          and_0(5,6) -> 4
          and_0(5,12) -> 4
          and_0(5,13) -> 4
          and_0(5,14) -> 4
          and_0(5,15) -> 4
          and_0(5,18) -> 4
          and_0(5,19) -> 4
          and_0(6,2) -> 4
          and_0(6,5) -> 4
          and_0(6,6) -> 4
          and_0(6,12) -> 4
          and_0(6,13) -> 4
          and_0(6,14) -> 4
          and_0(6,15) -> 4
          and_0(6,18) -> 4
          and_0(6,19) -> 4
          and_0(12,2) -> 4
          and_0(12,5) -> 4
          and_0(12,6) -> 4
          and_0(12,12) -> 4
          and_0(12,13) -> 4
          and_0(12,14) -> 4
          and_0(12,15) -> 4
          and_0(12,18) -> 4
          and_0(12,19) -> 4
          and_0(13,2) -> 4
          and_0(13,5) -> 4
          and_0(13,6) -> 4
          and_0(13,12) -> 4
          and_0(13,13) -> 4
          and_0(13,14) -> 4
          and_0(13,15) -> 4
          and_0(13,18) -> 4
          and_0(13,19) -> 4
          and_0(14,2) -> 4
          and_0(14,5) -> 4
          and_0(14,6) -> 4
          and_0(14,12) -> 4
          and_0(14,13) -> 4
          and_0(14,14) -> 4
          and_0(14,15) -> 4
          and_0(14,18) -> 4
          and_0(14,19) -> 4
          and_0(15,2) -> 4
          and_0(15,5) -> 4
          and_0(15,6) -> 4
          and_0(15,12) -> 4
          and_0(15,13) -> 4
          and_0(15,14) -> 4
          and_0(15,15) -> 4
          and_0(15,18) -> 4
          and_0(15,19) -> 4
          and_0(18,2) -> 4
          and_0(18,5) -> 4
          and_0(18,6) -> 4
          and_0(18,12) -> 4
          and_0(18,13) -> 4
          and_0(18,14) -> 4
          and_0(18,15) -> 4
          and_0(18,18) -> 4
          and_0(18,19) -> 4
          and_0(19,2) -> 4
          and_0(19,5) -> 4
          and_0(19,6) -> 4
          and_0(19,12) -> 4
          and_0(19,13) -> 4
          and_0(19,14) -> 4
          and_0(19,15) -> 4
          and_0(19,18) -> 4
          and_0(19,19) -> 4
          and_1(2,2) -> 21
          and_1(2,5) -> 21
          and_1(2,6) -> 21
          and_1(2,12) -> 21
          and_1(2,13) -> 21
          and_1(2,14) -> 21
          and_1(2,15) -> 21
          and_1(2,18) -> 21
          and_1(2,19) -> 21
          and_1(5,2) -> 21
          and_1(5,5) -> 21
          and_1(5,6) -> 21
          and_1(5,12) -> 21
          and_1(5,13) -> 21
          and_1(5,14) -> 21
          and_1(5,15) -> 21
          and_1(5,18) -> 21
          and_1(5,19) -> 21
          and_1(6,2) -> 21
          and_1(6,5) -> 21
          and_1(6,6) -> 21
          and_1(6,12) -> 21
          and_1(6,13) -> 21
          and_1(6,14) -> 21
          and_1(6,15) -> 21
          and_1(6,18) -> 21
          and_1(6,19) -> 21
          and_1(12,2) -> 21
          and_1(12,5) -> 21
          and_1(12,6) -> 21
          and_1(12,12) -> 21
          and_1(12,13) -> 21
          and_1(12,14) -> 21
          and_1(12,15) -> 21
          and_1(12,18) -> 21
          and_1(12,19) -> 21
          and_1(13,2) -> 21
          and_1(13,5) -> 21
          and_1(13,6) -> 21
          and_1(13,12) -> 21
          and_1(13,13) -> 21
          and_1(13,14) -> 21
          and_1(13,15) -> 21
          and_1(13,18) -> 21
          and_1(13,19) -> 21
          and_1(14,2) -> 21
          and_1(14,5) -> 21
          and_1(14,6) -> 21
          and_1(14,12) -> 21
          and_1(14,13) -> 21
          and_1(14,14) -> 21
          and_1(14,15) -> 21
          and_1(14,18) -> 21
          and_1(14,19) -> 21
          and_1(15,2) -> 21
          and_1(15,5) -> 21
          and_1(15,6) -> 21
          and_1(15,12) -> 21
          and_1(15,13) -> 21
          and_1(15,14) -> 21
          and_1(15,15) -> 21
          and_1(15,18) -> 21
          and_1(15,19) -> 21
          and_1(18,2) -> 21
          and_1(18,5) -> 21
          and_1(18,6) -> 21
          and_1(18,12) -> 21
          and_1(18,13) -> 21
          and_1(18,14) -> 21
          and_1(18,15) -> 21
          and_1(18,18) -> 21
          and_1(18,19) -> 21
          and_1(19,2) -> 21
          and_1(19,5) -> 21
          and_1(19,6) -> 21
          and_1(19,12) -> 21
          and_1(19,13) -> 21
          and_1(19,14) -> 21
          and_1(19,15) -> 21
          and_1(19,18) -> 21
          and_1(19,19) -> 21
          e_0() -> 5
          e_1() -> 27
          i_0() -> 6
          i_1() -> 27
          isList_0(2) -> 7
          isList_0(5) -> 7
          isList_0(6) -> 7
          isList_0(12) -> 7
          isList_0(13) -> 7
          isList_0(14) -> 7
          isList_0(15) -> 7
          isList_0(18) -> 7
          isList_0(19) -> 7
          isList_1(2) -> 22
          isList_1(5) -> 22
          isList_1(6) -> 22
          isList_1(12) -> 22
          isList_1(13) -> 22
          isList_1(14) -> 22
          isList_1(15) -> 22
          isList_1(18) -> 22
          isList_1(19) -> 22
          isNeList_0(2) -> 8
          isNeList_0(5) -> 8
          isNeList_0(6) -> 8
          isNeList_0(12) -> 8
          isNeList_0(13) -> 8
          isNeList_0(14) -> 8
          isNeList_0(15) -> 8
          isNeList_0(18) -> 8
          isNeList_0(19) -> 8
          isNeList_1(2) -> 23
          isNeList_1(5) -> 23
          isNeList_1(6) -> 23
          isNeList_1(12) -> 23
          isNeList_1(13) -> 23
          isNeList_1(14) -> 23
          isNeList_1(15) -> 23
          isNeList_1(18) -> 23
          isNeList_1(19) -> 23
          isNePal_0(2) -> 9
          isNePal_0(5) -> 9
          isNePal_0(6) -> 9
          isNePal_0(12) -> 9
          isNePal_0(13) -> 9
          isNePal_0(14) -> 9
          isNePal_0(15) -> 9
          isNePal_0(18) -> 9
          isNePal_0(19) -> 9
          isNePal_1(2) -> 24
          isNePal_1(5) -> 24
          isNePal_1(6) -> 24
          isNePal_1(12) -> 24
          isNePal_1(13) -> 24
          isNePal_1(14) -> 24
          isNePal_1(15) -> 24
          isNePal_1(18) -> 24
          isNePal_1(19) -> 24
          isPal_0(2) -> 10
          isPal_0(5) -> 10
          isPal_0(6) -> 10
          isPal_0(12) -> 10
          isPal_0(13) -> 10
          isPal_0(14) -> 10
          isPal_0(15) -> 10
          isPal_0(18) -> 10
          isPal_0(19) -> 10
          isPal_1(2) -> 25
          isPal_1(5) -> 25
          isPal_1(6) -> 25
          isPal_1(12) -> 25
          isPal_1(13) -> 25
          isPal_1(14) -> 25
          isPal_1(15) -> 25
          isPal_1(18) -> 25
          isPal_1(19) -> 25
          isQid_0(2) -> 11
          isQid_0(5) -> 11
          isQid_0(6) -> 11
          isQid_0(12) -> 11
          isQid_0(13) -> 11
          isQid_0(14) -> 11
          isQid_0(15) -> 11
          isQid_0(18) -> 11
          isQid_0(19) -> 11
          isQid_1(2) -> 26
          isQid_1(5) -> 26
          isQid_1(6) -> 26
          isQid_1(12) -> 26
          isQid_1(13) -> 26
          isQid_1(14) -> 26
          isQid_1(15) -> 26
          isQid_1(18) -> 26
          isQid_1(19) -> 26
          mark_0(2) -> 12
          mark_0(5) -> 12
          mark_0(6) -> 12
          mark_0(12) -> 12
          mark_0(13) -> 12
          mark_0(14) -> 12
          mark_0(15) -> 12
          mark_0(18) -> 12
          mark_0(19) -> 12
          mark_1(20) -> 1
          mark_1(20) -> 20
          mark_1(21) -> 4
          mark_1(21) -> 21
          nil_0() -> 13
          nil_1() -> 27
          o_0() -> 14
          o_1() -> 27
          ok_0(2) -> 15
          ok_0(5) -> 15
          ok_0(6) -> 15
          ok_0(12) -> 15
          ok_0(13) -> 15
          ok_0(14) -> 15
          ok_0(15) -> 15
          ok_0(18) -> 15
          ok_0(19) -> 15
          ok_1(20) -> 1
          ok_1(20) -> 20
          ok_1(21) -> 4
          ok_1(21) -> 21
          ok_1(22) -> 7
          ok_1(22) -> 22
          ok_1(23) -> 8
          ok_1(23) -> 23
          ok_1(24) -> 9
          ok_1(24) -> 24
          ok_1(25) -> 10
          ok_1(25) -> 25
          ok_1(26) -> 11
          ok_1(26) -> 26
          ok_1(27) -> 16
          ok_1(27) -> 28
          proper_0(2) -> 16
          proper_0(5) -> 16
          proper_0(6) -> 16
          proper_0(12) -> 16
          proper_0(13) -> 16
          proper_0(14) -> 16
          proper_0(15) -> 16
          proper_0(18) -> 16
          proper_0(19) -> 16
          proper_1(2) -> 28
          proper_1(5) -> 28
          proper_1(6) -> 28
          proper_1(12) -> 28
          proper_1(13) -> 28
          proper_1(14) -> 28
          proper_1(15) -> 28
          proper_1(18) -> 28
          proper_1(19) -> 28
          top_0(2) -> 17
          top_0(5) -> 17
          top_0(6) -> 17
          top_0(12) -> 17
          top_0(13) -> 17
          top_0(14) -> 17
          top_0(15) -> 17
          top_0(18) -> 17
          top_0(19) -> 17
          top_1(28) -> 17
          top_2(29) -> 17
          tt_0() -> 18
          tt_1() -> 27
          u_0() -> 19
          u_1() -> 27
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            __(X1,mark(X2)) -> mark(__(X1,X2))
            __(mark(X1),X2) -> mark(__(X1,X2))
            __(ok(X1),ok(X2)) -> ok(__(X1,X2))
            active(__(X,nil())) -> mark(X)
            active(__(X1,X2)) -> __(X1,active(X2))
            active(__(X1,X2)) -> __(active(X1),X2)
            active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
            active(__(nil(),X)) -> mark(X)
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(isList(V)) -> mark(isNeList(V))
            active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2)))
            active(isList(nil())) -> mark(tt())
            active(isNeList(V)) -> mark(isQid(V))
            active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2)))
            active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2)))
            active(isNePal(V)) -> mark(isQid(V))
            active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P)))
            active(isPal(V)) -> mark(isNePal(V))
            active(isPal(nil())) -> mark(tt())
            active(isQid(a())) -> mark(tt())
            active(isQid(e())) -> mark(tt())
            active(isQid(i())) -> mark(tt())
            active(isQid(o())) -> mark(tt())
            active(isQid(u())) -> mark(tt())
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            isList(ok(X)) -> ok(isList(X))
            isNeList(ok(X)) -> ok(isNeList(X))
            isNePal(ok(X)) -> ok(isNePal(X))
            isPal(ok(X)) -> ok(isPal(X))
            isQid(ok(X)) -> ok(isQid(X))
            proper(__(X1,X2)) -> __(proper(X1),proper(X2))
            proper(a()) -> ok(a())
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(e()) -> ok(e())
            proper(i()) -> ok(i())
            proper(isList(X)) -> isList(proper(X))
            proper(isNeList(X)) -> isNeList(proper(X))
            proper(isNePal(X)) -> isNePal(proper(X))
            proper(isPal(X)) -> isPal(proper(X))
            proper(isQid(X)) -> isQid(proper(X))
            proper(nil()) -> ok(nil())
            proper(o()) -> ok(o())
            proper(tt()) -> ok(tt())
            proper(u()) -> ok(u())
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {__/2,active/1,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1
            ,nil/0,o/0,ok/1,tt/0,u/0}
        - Obligation:
             runtime complexity wrt. defined symbols {__,active,and,isList,isNeList,isNePal,isPal,isQid,proper
            ,top} and constructors {a,e,i,mark,nil,o,ok,tt,u}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))