```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {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(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
c_0(1,1) -> 1
c_0(1,4) -> 1
c_0(4,1) -> 1
c_0(4,4) -> 1
c_1(1,6) -> 7
c_1(4,6) -> 7
c_1(6,1) -> 5
c_1(6,4) -> 5
c_1(10,1) -> 7
c_1(10,4) -> 7
c_2(9,1) -> 8
c_2(9,4) -> 8
c_2(9,6) -> 8
f_0(1) -> 2
f_0(4) -> 2
f_1(5) -> 2
f_1(7) -> 3
f_2(8) -> 3
g_0(1) -> 3
g_0(4) -> 3
s_0(1) -> 4
s_0(4) -> 4
s_1(1) -> 6
s_1(4) -> 6
s_1(6) -> 6
s_1(9) -> 10
s_1(10) -> 10
s_2(1) -> 9
s_2(4) -> 9
s_2(9) -> 9
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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