```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(a(),a()) -> f(a(),b())
f(a(),b()) -> f(s(a()),c())
f(c(),c()) -> f(a(),a())
f(s(X),c()) -> f(X,c())
- Signature:
{f/2} / {a/0,b/0,c/0,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
+ 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:
f(a(),a()) -> f(a(),b())
f(a(),b()) -> f(s(a()),c())
f(c(),c()) -> f(a(),a())
f(s(X),c()) -> f(X,c())
- Signature:
{f/2} / {a/0,b/0,c/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
a_0() -> 2
a_1() -> 3
a_2() -> 7
a_3() -> 10
b_0() -> 2
b_1() -> 4
b_2() -> 9
c_0() -> 2
c_1() -> 4
c_2() -> 6
c_3() -> 8
c_4() -> 11
f_0(2,2) -> 1
f_1(2,4) -> 1
f_1(3,3) -> 1
f_1(3,4) -> 1
f_2(3,6) -> 1
f_2(5,6) -> 1
f_2(7,9) -> 1
f_3(7,8) -> 1
f_4(10,11) -> 1
s_0(2) -> 2
s_1(3) -> 3
s_2(7) -> 5
s_3(10) -> 7
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(a(),a()) -> f(a(),b())
f(a(),b()) -> f(s(a()),c())
f(c(),c()) -> f(a(),a())
f(s(X),c()) -> f(X,c())
- Signature:
{f/2} / {a/0,b/0,c/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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