```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__d(X)) -> d(X)
activate(n__f(X)) -> f(X)
c(X) -> d(activate(X))
d(X) -> n__d(X)
f(X) -> n__f(X)
f(f(X)) -> c(n__f(g(n__f(X))))
h(X) -> c(n__d(X))
- Signature:
{activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1}
- Obligation:
runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
activate_0(5) -> 1
activate_0(7) -> 1
activate_0(8) -> 1
activate_1(5) -> 9
activate_1(7) -> 9
activate_1(8) -> 9
activate_2(3) -> 10
c_0(5) -> 2
c_0(7) -> 2
c_0(8) -> 2
c_1(3) -> 6
d_0(5) -> 3
d_0(5) -> 10
d_0(7) -> 3
d_0(7) -> 10
d_0(8) -> 3
d_0(8) -> 10
d_1(5) -> 1
d_1(5) -> 9
d_1(7) -> 1
d_1(7) -> 9
d_1(8) -> 1
d_1(8) -> 9
d_1(9) -> 2
d_2(5) -> 10
d_2(7) -> 10
d_2(8) -> 10
d_2(10) -> 6
f_0(5) -> 4
f_0(7) -> 4
f_0(8) -> 4
f_1(5) -> 1
f_1(5) -> 9
f_1(7) -> 1
f_1(7) -> 9
f_1(8) -> 1
f_1(8) -> 9
g_0(5) -> 1
g_0(5) -> 5
g_0(5) -> 9
g_0(7) -> 1
g_0(7) -> 5
g_0(7) -> 9
g_0(8) -> 1
g_0(8) -> 5
g_0(8) -> 9
h_0(5) -> 6
h_0(7) -> 6
h_0(8) -> 6
n__d_0(5) -> 1
n__d_0(5) -> 7
n__d_0(5) -> 9
n__d_0(7) -> 1
n__d_0(7) -> 7
n__d_0(7) -> 9
n__d_0(8) -> 1
n__d_0(8) -> 7
n__d_0(8) -> 9
n__d_1(5) -> 3
n__d_1(5) -> 10
n__d_1(7) -> 3
n__d_1(7) -> 10
n__d_1(8) -> 3
n__d_1(8) -> 10
n__d_2(5) -> 1
n__d_2(5) -> 9
n__d_2(7) -> 1
n__d_2(7) -> 9
n__d_2(8) -> 1
n__d_2(8) -> 9
n__d_2(9) -> 2
n__d_3(5) -> 10
n__d_3(7) -> 10
n__d_3(8) -> 10
n__d_3(10) -> 6
n__f_0(5) -> 1
n__f_0(5) -> 8
n__f_0(5) -> 9
n__f_0(7) -> 1
n__f_0(7) -> 8
n__f_0(7) -> 9
n__f_0(8) -> 1
n__f_0(8) -> 8
n__f_0(8) -> 9
n__f_1(5) -> 4
n__f_1(7) -> 4
n__f_1(8) -> 4
n__f_2(5) -> 1
n__f_2(5) -> 9
n__f_2(7) -> 1
n__f_2(7) -> 9
n__f_2(8) -> 1
n__f_2(8) -> 9
3 -> 10
5 -> 1
5 -> 9
7 -> 1
7 -> 9
8 -> 1
8 -> 9
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__d(X)) -> d(X)
activate(n__f(X)) -> f(X)
c(X) -> d(activate(X))
d(X) -> n__d(X)
f(X) -> n__f(X)
f(f(X)) -> c(n__f(g(n__f(X))))
h(X) -> c(n__d(X))
- Signature:
{activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1}
- Obligation:
runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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