```* 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))
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(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
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,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,active/1,e/0,i/0,mark/1
,nil/0,o/0,ok/1,tt/0,u/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {__,and,isList,isNeList,isNePal,isPal,isQid,proper
,top} and constructors {a,active,e,i,mark,nil,o,ok,tt,u}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
___0(2,2) -> 1
___1(2,2) -> 3
a_0() -> 2
a_1() -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
and_0(2,2) -> 1
and_1(2,2) -> 3
e_0() -> 2
e_1() -> 3
i_0() -> 2
i_1() -> 3
isList_0(2) -> 1
isList_1(2) -> 3
isNeList_0(2) -> 1
isNeList_1(2) -> 3
isNePal_0(2) -> 1
isNePal_1(2) -> 3
isPal_0(2) -> 1
isPal_1(2) -> 3
isQid_0(2) -> 1
isQid_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
nil_0() -> 2
nil_1() -> 3
o_0() -> 2
o_1() -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
proper_0(2) -> 1
proper_1(2) -> 4
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
tt_0() -> 2
tt_1() -> 3
u_0() -> 2
u_1() -> 3
* 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))
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(a()) -> ok(a())
proper(e()) -> ok(e())
proper(i()) -> ok(i())
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,and/2,isList/1,isNeList/1,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,active/1,e/0,i/0,mark/1
,nil/0,o/0,ok/1,tt/0,u/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {__,and,isList,isNeList,isNePal,isPal,isQid,proper
,top} and constructors {a,active,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))
```