```* Step 1: ToInnermost WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
b(u(x)) -> a(e(x))
c(u(x)) -> b(x)
d(x) -> e(u(x))
d(u(x)) -> c(x)
v(e(x)) -> x
- Signature:
{b/1,c/1,d/1,v/1} / {a/1,e/1,u/1}
- Obligation:
runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u}
+ Applied Processor:
ToInnermost
+ Details:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
b(u(x)) -> a(e(x))
c(u(x)) -> b(x)
d(x) -> e(u(x))
d(u(x)) -> c(x)
v(e(x)) -> x
- Signature:
{b/1,c/1,d/1,v/1} / {a/1,e/1,u/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:

Strict DPs
b#(u(x)) -> c_1()
c#(u(x)) -> c_2(b#(x))
d#(x) -> c_3()
d#(u(x)) -> c_4(c#(x))
v#(e(x)) -> c_5()
Weak DPs

and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
b#(u(x)) -> c_1()
c#(u(x)) -> c_2(b#(x))
d#(x) -> c_3()
d#(u(x)) -> c_4(c#(x))
v#(e(x)) -> c_5()
- Weak TRS:
b(u(x)) -> a(e(x))
c(u(x)) -> b(x)
d(x) -> e(u(x))
d(u(x)) -> c(x)
v(e(x)) -> x
- Signature:
{b/1,c/1,d/1,v/1,b#/1,c#/1,d#/1,v#/1} / {a/1,e/1,u/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {b#,c#,d#,v#} and constructors {a,e,u}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
b#(u(x)) -> c_1()
c#(u(x)) -> c_2(b#(x))
d#(x) -> c_3()
d#(u(x)) -> c_4(c#(x))
v#(e(x)) -> c_5()
* Step 4: Trivial WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
b#(u(x)) -> c_1()
c#(u(x)) -> c_2(b#(x))
d#(x) -> c_3()
d#(u(x)) -> c_4(c#(x))
v#(e(x)) -> c_5()
- Signature:
{b/1,c/1,d/1,v/1,b#/1,c#/1,d#/1,v#/1} / {a/1,e/1,u/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {b#,c#,d#,v#} and constructors {a,e,u}
+ Applied Processor:
Trivial
+ Details:
Consider the dependency graph
1:S:b#(u(x)) -> c_1()

2:S:c#(u(x)) -> c_2(b#(x))
-->_1 b#(u(x)) -> c_1():1

3:S:d#(x) -> c_3()

4:S:d#(u(x)) -> c_4(c#(x))
-->_1 c#(u(x)) -> c_2(b#(x)):2

5:S:v#(e(x)) -> c_5()

The dependency graph contains no loops, we remove all dependency pairs.
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:

- Signature:
{b/1,c/1,d/1,v/1,b#/1,c#/1,d#/1,v#/1} / {a/1,e/1,u/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {b#,c#,d#,v#} and constructors {a,e,u}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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