```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
U11(mark(X)) -> mark(U11(X))
U11(ok(X)) -> ok(U11(X))
U12(mark(X)) -> mark(U12(X))
U12(ok(X)) -> ok(U12(X))
__(X1,mark(X2)) -> mark(__(X1,X2))
__(mark(X1),X2) -> mark(__(X1,X2))
__(ok(X1),ok(X2)) -> ok(__(X1,X2))
active(U11(X)) -> U11(active(X))
active(U11(tt())) -> mark(U12(tt()))
active(U12(X)) -> U12(active(X))
active(U12(tt())) -> mark(tt())
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(isNePal(X)) -> isNePal(active(X))
active(isNePal(__(I,__(P,I)))) -> mark(U11(tt()))
isNePal(mark(X)) -> mark(isNePal(X))
isNePal(ok(X)) -> ok(isNePal(X))
proper(U11(X)) -> U11(proper(X))
proper(U12(X)) -> U12(proper(X))
proper(__(X1,X2)) -> __(proper(X1),proper(X2))
proper(isNePal(X)) -> isNePal(proper(X))
proper(nil()) -> ok(nil())
proper(tt()) -> ok(tt())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0}
- Obligation:
runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil
,ok,tt}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
U11_0(6) -> 1
U11_0(7) -> 1
U11_0(8) -> 1
U11_0(11) -> 1
U11_1(6) -> 12
U11_1(7) -> 12
U11_1(8) -> 12
U11_1(11) -> 12
U12_0(6) -> 2
U12_0(7) -> 2
U12_0(8) -> 2
U12_0(11) -> 2
U12_1(6) -> 13
U12_1(7) -> 13
U12_1(8) -> 13
U12_1(11) -> 13
___0(6,6) -> 3
___0(6,7) -> 3
___0(6,8) -> 3
___0(6,11) -> 3
___0(7,6) -> 3
___0(7,7) -> 3
___0(7,8) -> 3
___0(7,11) -> 3
___0(8,6) -> 3
___0(8,7) -> 3
___0(8,8) -> 3
___0(8,11) -> 3
___0(11,6) -> 3
___0(11,7) -> 3
___0(11,8) -> 3
___0(11,11) -> 3
___1(6,6) -> 14
___1(6,7) -> 14
___1(6,8) -> 14
___1(6,11) -> 14
___1(7,6) -> 14
___1(7,7) -> 14
___1(7,8) -> 14
___1(7,11) -> 14
___1(8,6) -> 14
___1(8,7) -> 14
___1(8,8) -> 14
___1(8,11) -> 14
___1(11,6) -> 14
___1(11,7) -> 14
___1(11,8) -> 14
___1(11,11) -> 14
active_0(6) -> 4
active_0(7) -> 4
active_0(8) -> 4
active_0(11) -> 4
active_1(6) -> 17
active_1(7) -> 17
active_1(8) -> 17
active_1(11) -> 17
active_2(16) -> 18
isNePal_0(6) -> 5
isNePal_0(7) -> 5
isNePal_0(8) -> 5
isNePal_0(11) -> 5
isNePal_1(6) -> 15
isNePal_1(7) -> 15
isNePal_1(8) -> 15
isNePal_1(11) -> 15
mark_0(6) -> 6
mark_0(7) -> 6
mark_0(8) -> 6
mark_0(11) -> 6
mark_1(12) -> 1
mark_1(12) -> 12
mark_1(13) -> 2
mark_1(13) -> 13
mark_1(14) -> 3
mark_1(14) -> 14
mark_1(15) -> 5
mark_1(15) -> 15
nil_0() -> 7
nil_1() -> 16
ok_0(6) -> 8
ok_0(7) -> 8
ok_0(8) -> 8
ok_0(11) -> 8
ok_1(12) -> 1
ok_1(12) -> 12
ok_1(13) -> 2
ok_1(13) -> 13
ok_1(14) -> 3
ok_1(14) -> 14
ok_1(15) -> 5
ok_1(15) -> 15
ok_1(16) -> 9
ok_1(16) -> 17
proper_0(6) -> 9
proper_0(7) -> 9
proper_0(8) -> 9
proper_0(11) -> 9
proper_1(6) -> 17
proper_1(7) -> 17
proper_1(8) -> 17
proper_1(11) -> 17
top_0(6) -> 10
top_0(7) -> 10
top_0(8) -> 10
top_0(11) -> 10
top_1(17) -> 10
top_2(18) -> 10
tt_0() -> 11
tt_1() -> 16
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
U11(mark(X)) -> mark(U11(X))
U11(ok(X)) -> ok(U11(X))
U12(mark(X)) -> mark(U12(X))
U12(ok(X)) -> ok(U12(X))
__(X1,mark(X2)) -> mark(__(X1,X2))
__(mark(X1),X2) -> mark(__(X1,X2))
__(ok(X1),ok(X2)) -> ok(__(X1,X2))
active(U11(X)) -> U11(active(X))
active(U11(tt())) -> mark(U12(tt()))
active(U12(X)) -> U12(active(X))
active(U12(tt())) -> mark(tt())
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(isNePal(X)) -> isNePal(active(X))
active(isNePal(__(I,__(P,I)))) -> mark(U11(tt()))
isNePal(mark(X)) -> mark(isNePal(X))
isNePal(ok(X)) -> ok(isNePal(X))
proper(U11(X)) -> U11(proper(X))
proper(U12(X)) -> U12(proper(X))
proper(__(X1,X2)) -> __(proper(X1),proper(X2))
proper(isNePal(X)) -> isNePal(proper(X))
proper(nil()) -> ok(nil())
proper(tt()) -> ok(tt())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0}
- Obligation:
runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil
,ok,tt}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))
```