* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
- Signature:
{c/3} / {a/0,b/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {c} and constructors {a,b}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:
Strict DPs
c#(b(a(),a()),b(y,z),x) -> c_1()
Weak DPs
and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
c#(b(a(),a()),b(y,z),x) -> c_1()
- Weak TRS:
c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
- Signature:
{c/3,c#/3} / {a/0,b/2,c_1/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {c#} and constructors {a,b}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
c#(b(a(),a()),b(y,z),x) -> c_1()
* Step 3: Trivial WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
c#(b(a(),a()),b(y,z),x) -> c_1()
- Signature:
{c/3,c#/3} / {a/0,b/2,c_1/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {c#} and constructors {a,b}
+ Applied Processor:
Trivial
+ Details:
Consider the dependency graph
1:S:c#(b(a(),a()),b(y,z),x) -> c_1()
The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Signature:
{c/3,c#/3} / {a/0,b/2,c_1/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {c#} and constructors {a,b}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(1))