```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
e(g(X)) -> e(X)
f(a()) -> f(c(a()))
f(a()) -> f(d(a()))
f(c(X)) -> X
f(c(a())) -> f(d(b()))
f(c(b())) -> f(d(a()))
f(d(X)) -> X
- Signature:
{e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
- Obligation:
runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,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:
e(g(X)) -> e(X)
f(a()) -> f(c(a()))
f(a()) -> f(d(a()))
f(c(X)) -> X
f(c(a())) -> f(d(b()))
f(c(b())) -> f(d(a()))
f(d(X)) -> X
- Signature:
{e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_0() -> 2
a_1() -> 1
a_1() -> 4
a_2() -> 1
a_2() -> 6
b_0() -> 1
b_0() -> 2
b_1() -> 1
b_1() -> 4
b_2() -> 1
b_2() -> 6
c_0(2) -> 1
c_0(2) -> 2
c_1(4) -> 3
d_0(2) -> 1
d_0(2) -> 2
d_1(4) -> 3
d_2(6) -> 5
e_0(2) -> 1
e_1(2) -> 1
f_0(2) -> 1
f_1(3) -> 1
f_2(5) -> 1
g_0(2) -> 1
g_0(2) -> 2
2 -> 1
4 -> 1
6 -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
e(g(X)) -> e(X)
f(a()) -> f(c(a()))
f(a()) -> f(d(a()))
f(c(X)) -> X
f(c(a())) -> f(d(b()))
f(c(b())) -> f(d(a()))
f(d(X)) -> X
- Signature:
{e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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