* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6)
foldl#3(x2,Nil()) -> x2
main(x1) -> foldl#3(Nil(),x1)
- Signature:
{foldl#3/2,main/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6)
foldl#3(x2,Nil()) -> x2
main(x1) -> foldl#3(Nil(),x1)
- Signature:
{foldl#3/2,main/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
foldl#3(x,z){z -> Cons(y,z)} =
foldl#3(x,Cons(y,z)) ->^+ foldl#3(Cons(y,x),z)
= C[foldl#3(Cons(y,x),z) = foldl#3(x,z){x -> Cons(y,x)}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6)
foldl#3(x2,Nil()) -> x2
main(x1) -> foldl#3(Nil(),x1)
- Signature:
{foldl#3/2,main/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil}
+ 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) -> 1
Cons_0(2,2) -> 2
Cons_1(2,2) -> 1
Cons_1(2,2) -> 3
Cons_1(2,3) -> 1
Cons_1(2,3) -> 3
Nil_0() -> 1
Nil_0() -> 2
Nil_1() -> 1
Nil_1() -> 3
foldl#3_0(2,2) -> 1
foldl#3_1(3,2) -> 1
main_0(2) -> 1
2 -> 1
3 -> 1
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
foldl#3(x16,Cons(x24,x6)) -> foldl#3(Cons(x24,x16),x6)
foldl#3(x2,Nil()) -> x2
main(x1) -> foldl#3(Nil(),x1)
- Signature:
{foldl#3/2,main/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {foldl#3,main} and constructors {Cons,Nil}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))