```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(s(X)) -> f(X)
g(cons(0(),Y)) -> g(Y)
g(cons(s(X),Y)) -> s(X)
h(cons(X,Y)) -> h(g(cons(X,Y)))
- Signature:
{f/1,g/1,h/1} / {0/0,cons/2,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,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(s(X)) -> f(X)
g(cons(0(),Y)) -> g(Y)
g(cons(s(X),Y)) -> s(X)
h(cons(X,Y)) -> h(g(cons(X,Y)))
- Signature:
{f/1,g/1,h/1} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
cons_0(2,2) -> 2
cons_1(2,2) -> 4
f_0(2) -> 1
f_1(2) -> 1
g_0(2) -> 1
g_1(2) -> 1
g_1(2) -> 3
g_1(4) -> 3
h_0(2) -> 1
h_1(3) -> 1
s_0(2) -> 2
s_1(2) -> 1
s_1(2) -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(s(X)) -> f(X)
g(cons(0(),Y)) -> g(Y)
g(cons(s(X),Y)) -> s(X)
h(cons(X,Y)) -> h(g(cons(X,Y)))
- Signature:
{f/1,g/1,h/1} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,cons,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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