* Step 1: Sum WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
even(0()) -> S(0())
even(S(x)) -> odd(x)
odd(0()) -> 0()
odd(S(x)) -> even(x)
- Signature:
{even/1,odd/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
even(0()) -> S(0())
even(S(x)) -> odd(x)
odd(0()) -> 0()
odd(S(x)) -> even(x)
- Signature:
{even/1,odd/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
0_1() -> 1
0_1() -> 3
S_0(2) -> 2
S_1(3) -> 1
even_0(2) -> 1
even_1(2) -> 1
odd_0(2) -> 1
odd_1(2) -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
even(0()) -> S(0())
even(S(x)) -> odd(x)
odd(0()) -> 0()
odd(S(x)) -> even(x)
- Signature:
{even/1,odd/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))