* Step 1: DependencyPairs WORST_CASE(?,O(1))
+ Considered Problem:
- Strict TRS:
t(x) -> x
t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
- Signature:
{t/1} / {0/0,c/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {t} and constructors {0,c}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:
Strict DPs
t#(x) -> c_1()
t#(x) -> c_2()
Weak DPs
and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
t#(x) -> c_1()
t#(x) -> c_2()
- Weak TRS:
t(x) -> x
t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
- Signature:
{t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
t#(x) -> c_1()
t#(x) -> c_2()
* Step 3: Trivial WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
t#(x) -> c_1()
t#(x) -> c_2()
- Signature:
{t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c}
+ Applied Processor:
Trivial
+ Details:
Consider the dependency graph
1:S:t#(x) -> c_1()
2:S:t#(x) -> c_2()
The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Signature:
{t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(1))