```* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
- Signature:
{f/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:

Strict DPs
f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
Weak DPs

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

2:S:f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))

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

- Signature:
{f/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/2,c_2/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {f#} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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