```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
check(no(x)) -> no(x)
check(no(x)) -> no(check(x))
check(rec(x)) -> rec(check(x))
check(sent(x)) -> sent(check(x))
check(up(x)) -> up(check(x))
no(up(x)) -> up(no(x))
rec(bot()) -> up(sent(bot()))
rec(no(x)) -> sent(rec(x))
rec(rec(x)) -> sent(rec(x))
rec(sent(x)) -> sent(rec(x))
rec(up(x)) -> up(rec(x))
sent(up(x)) -> up(sent(x))
top(no(up(x))) -> top(check(rec(x)))
top(rec(up(x))) -> top(check(rec(x)))
top(sent(up(x))) -> top(check(rec(x)))
- Signature:
{check/1,no/1,rec/1,sent/1,top/1} / {bot/0,up/1}
- Obligation:
runtime complexity wrt. defined symbols {check,no,rec,sent,top} and constructors {bot,up}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
bot_0() -> 2
bot_1() -> 4
check_0(2) -> 1
check_1(2) -> 3
no_0(2) -> 1
no_1(2) -> 3
rec_0(2) -> 1
rec_1(2) -> 3
sent_0(2) -> 1
sent_1(2) -> 3
sent_1(4) -> 3
top_0(2) -> 1
up_0(2) -> 2
up_1(3) -> 1
up_1(3) -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
check(no(x)) -> no(x)
check(no(x)) -> no(check(x))
check(rec(x)) -> rec(check(x))
check(sent(x)) -> sent(check(x))
check(up(x)) -> up(check(x))
no(up(x)) -> up(no(x))
rec(bot()) -> up(sent(bot()))
rec(no(x)) -> sent(rec(x))
rec(rec(x)) -> sent(rec(x))
rec(sent(x)) -> sent(rec(x))
rec(up(x)) -> up(rec(x))
sent(up(x)) -> up(sent(x))
top(no(up(x))) -> top(check(rec(x)))
top(rec(up(x))) -> top(check(rec(x)))
top(sent(up(x))) -> top(check(rec(x)))
- Signature:
{check/1,no/1,rec/1,sent/1,top/1} / {bot/0,up/1}
- Obligation:
runtime complexity wrt. defined symbols {check,no,rec,sent,top} and constructors {bot,up}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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