```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a() -> n__a()
activate(X) -> X
activate(n__a()) -> a()
activate(n__f(X)) -> f(X)
activate(n__g(X)) -> g(activate(X))
f(X) -> n__f(X)
f(n__f(n__a())) -> f(n__g(n__f(n__a())))
g(X) -> n__g(X)
- Signature:
{a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
- Obligation:
runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
+ 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:
a() -> n__a()
activate(X) -> X
activate(n__a()) -> a()
activate(n__f(X)) -> f(X)
activate(n__g(X)) -> g(activate(X))
f(X) -> n__f(X)
f(n__f(n__a())) -> f(n__g(n__f(n__a())))
g(X) -> n__g(X)
- Signature:
{a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 1
a_1() -> 3
activate_0(2) -> 1
activate_1(2) -> 3
activate_1(4) -> 3
activate_2(4) -> 5
f_0(2) -> 1
f_1(2) -> 1
f_1(2) -> 3
f_1(3) -> 5
f_2(1) -> 3
f_2(1) -> 5
g_0(2) -> 1
g_1(3) -> 1
g_1(3) -> 3
g_2(5) -> 3
n__a_0() -> 1
n__a_0() -> 2
n__a_0() -> 3
n__a_1() -> 1
n__a_2() -> 1
n__a_2() -> 3
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_0(2) -> 3
n__f_1(1) -> 3
n__f_1(1) -> 4
n__f_1(1) -> 5
n__f_1(2) -> 1
n__f_2(2) -> 1
n__f_2(2) -> 3
n__f_2(3) -> 5
n__f_3(1) -> 3
n__f_3(1) -> 5
n__g_0(2) -> 1
n__g_0(2) -> 2
n__g_0(2) -> 3
n__g_1(2) -> 1
n__g_1(4) -> 1
n__g_1(4) -> 2
n__g_1(4) -> 3
n__g_2(3) -> 1
n__g_2(3) -> 3
n__g_2(5) -> 1
n__g_3(5) -> 3
2 -> 1
2 -> 3
4 -> 3
4 -> 5
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a() -> n__a()
activate(X) -> X
activate(n__a()) -> a()
activate(n__f(X)) -> f(X)
activate(n__g(X)) -> g(activate(X))
f(X) -> n__f(X)
f(n__f(n__a())) -> f(n__g(n__f(n__a())))
g(X) -> n__g(X)
- Signature:
{a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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