```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a(b(x)) -> b(a(x))
a(c(x)) -> x
- Signature:
{a/1} / {b/1,c/1}
- Obligation:
runtime complexity wrt. defined symbols {a} and constructors {b,c}
+ 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(b(x)) -> b(a(x))
a(c(x)) -> x
- Signature:
{a/1} / {b/1,c/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
a_0(2) -> 1
a_1(2) -> 3
b_0(2) -> 1
b_0(2) -> 2
b_0(2) -> 3
b_1(3) -> 1
b_1(3) -> 3
c_0(2) -> 1
c_0(2) -> 2
c_0(2) -> 3
2 -> 1
2 -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a(b(x)) -> b(a(x))
a(c(x)) -> x
- Signature:
{a/1} / {b/1,c/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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