```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
and(tt(),X) -> activate(X)
plus(N,0()) -> N
plus(N,s(M)) -> s(plus(N,M))
- Signature:
{activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
- Obligation:
runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
+ Applied Processor:
ToInnermost
+ Details:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
and(tt(),X) -> activate(X)
plus(N,0()) -> N
plus(N,s(M)) -> s(plus(N,M))
- Signature:
{activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 2
0_0() -> 3
activate_0(2) -> 1
activate_1(2) -> 1
and_0(2,2) -> 1
plus_0(2,2) -> 1
plus_1(2,2) -> 3
s_0(2) -> 1
s_0(2) -> 2
s_0(2) -> 3
s_1(3) -> 1
s_1(3) -> 3
tt_0() -> 1
tt_0() -> 2
tt_0() -> 3
2 -> 1
2 -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
and(tt(),X) -> activate(X)
plus(N,0()) -> N
plus(N,s(M)) -> s(plus(N,M))
- Signature:
{activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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