* Step 1: Sum WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
even(Cons(x,xs)) -> odd(xs)
even(Nil()) -> True()
evenodd(x) -> even(x)
notEmpty(Cons(x,xs)) -> True()
notEmpty(Nil()) -> False()
odd(Cons(x,xs)) -> even(xs)
odd(Nil()) -> False()
- Signature:
{even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False
,Nil,True}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
even(Cons(x,xs)) -> odd(xs)
even(Nil()) -> True()
evenodd(x) -> even(x)
notEmpty(Cons(x,xs)) -> True()
notEmpty(Nil()) -> False()
odd(Cons(x,xs)) -> even(xs)
odd(Nil()) -> False()
- Signature:
{even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False
,Nil,True}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
Cons_0(2,2) -> 2
False_0() -> 2
False_1() -> 1
Nil_0() -> 2
True_0() -> 2
True_1() -> 1
even_0(2) -> 1
even_1(2) -> 1
evenodd_0(2) -> 1
notEmpty_0(2) -> 1
odd_0(2) -> 1
odd_1(2) -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
even(Cons(x,xs)) -> odd(xs)
even(Nil()) -> True()
evenodd(x) -> even(x)
notEmpty(Cons(x,xs)) -> True()
notEmpty(Nil()) -> False()
odd(Cons(x,xs)) -> even(xs)
odd(Nil()) -> False()
- Signature:
{even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False
,Nil,True}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))