* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
anchored(Nil(),y) -> y
goal(x,y) -> anchored(x,y)
- Signature:
{anchored/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {anchored,goal} 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:
anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
anchored(Nil(),y) -> y
goal(x,y) -> anchored(x,y)
- Signature:
{anchored/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
anchored(y,z){y -> Cons(x,y)} =
anchored(Cons(x,y),z) ->^+ anchored(y,Cons(Cons(Nil(),Nil()),z))
= C[anchored(y,Cons(Cons(Nil(),Nil()),z)) = anchored(y,z){z -> Cons(Cons(Nil(),Nil()),z)}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
anchored(Nil(),y) -> y
goal(x,y) -> anchored(x,y)
- Signature:
{anchored/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
Cons_0(1,1) -> 1
Cons_0(1,1) -> 3
Cons_0(1,1) -> 4
Cons_0(1,2) -> 1
Cons_0(1,2) -> 3
Cons_0(1,2) -> 4
Cons_0(2,1) -> 1
Cons_0(2,1) -> 3
Cons_0(2,1) -> 4
Cons_0(2,2) -> 1
Cons_0(2,2) -> 3
Cons_0(2,2) -> 4
Cons_1(6,1) -> 3
Cons_1(6,1) -> 4
Cons_1(6,1) -> 5
Cons_1(6,2) -> 3
Cons_1(6,2) -> 4
Cons_1(6,2) -> 5
Cons_1(6,5) -> 3
Cons_1(6,5) -> 4
Cons_1(6,5) -> 5
Cons_1(7,8) -> 6
Nil_0() -> 2
Nil_0() -> 3
Nil_0() -> 4
Nil_1() -> 7
Nil_1() -> 8
anchored_0(1,1) -> 3
anchored_0(1,2) -> 3
anchored_0(2,1) -> 3
anchored_0(2,2) -> 3
anchored_1(1,1) -> 4
anchored_1(1,2) -> 4
anchored_1(1,5) -> 3
anchored_1(1,5) -> 4
anchored_1(2,1) -> 4
anchored_1(2,2) -> 4
anchored_1(2,5) -> 3
anchored_1(2,5) -> 4
goal_0(1,1) -> 4
goal_0(1,2) -> 4
goal_0(2,1) -> 4
goal_0(2,2) -> 4
1 -> 3
1 -> 4
2 -> 3
2 -> 4
5 -> 3
5 -> 4
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
anchored(Nil(),y) -> y
goal(x,y) -> anchored(x,y)
- Signature:
{anchored/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {anchored,goal} 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))