```* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
f(s(x)) -> s(s(f(h(s(x)))))
g(x,x) -> g(a(),b())
i(x,x) -> i(a(),b())
- Signature:
{f/1,g/2,i/2} / {a/0,b/0,h/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g,i} and constructors {a,b,h,s}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:

Strict DPs
f#(s(x)) -> c_1(f#(h(s(x))))
g#(x,x) -> c_2(g#(a(),b()))
i#(x,x) -> c_3(i#(a(),b()))
Weak DPs

and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
f#(s(x)) -> c_1(f#(h(s(x))))
g#(x,x) -> c_2(g#(a(),b()))
i#(x,x) -> c_3(i#(a(),b()))
- Weak TRS:
f(s(x)) -> s(s(f(h(s(x)))))
g(x,x) -> g(a(),b())
i(x,x) -> i(a(),b())
- Signature:
{f/1,g/2,i/2,f#/1,g#/2,i#/2} / {a/0,b/0,h/1,s/1,c_1/1,c_2/1,c_3/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f#,g#,i#} and constructors {a,b,h,s}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
f#(s(x)) -> c_1(f#(h(s(x))))
g#(x,x) -> c_2(g#(a(),b()))
i#(x,x) -> c_3(i#(a(),b()))
* Step 3: Trivial WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
f#(s(x)) -> c_1(f#(h(s(x))))
g#(x,x) -> c_2(g#(a(),b()))
i#(x,x) -> c_3(i#(a(),b()))
- Signature:
{f/1,g/2,i/2,f#/1,g#/2,i#/2} / {a/0,b/0,h/1,s/1,c_1/1,c_2/1,c_3/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f#,g#,i#} and constructors {a,b,h,s}
+ Applied Processor:
Trivial
+ Details:
Consider the dependency graph
1:S:f#(s(x)) -> c_1(f#(h(s(x))))

2:S:g#(x,x) -> c_2(g#(a(),b()))

3:S:i#(x,x) -> c_3(i#(a(),b()))

The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:

- Signature:
{f/1,g/2,i/2,f#/1,g#/2,i#/2} / {a/0,b/0,h/1,s/1,c_1/1,c_2/1,c_3/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f#,g#,i#} and constructors {a,b,h,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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