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