* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
ack(Cons(x,xs),Nil()) -> ack(xs,Cons(Nil(),Nil()))
ack(Cons(x',xs'),Cons(x,xs)) -> ack(xs',ack(Cons(x',xs'),xs))
ack(Nil(),n) -> Cons(Cons(Nil(),Nil()),n)
goal(m,n) -> ack(m,n)
- Signature:
{ack/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {ack,goal} and constructors {Cons,Nil}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
ack(Cons(x,xs),Nil()) -> ack(xs,Cons(Nil(),Nil()))
ack(Cons(x',xs'),Cons(x,xs)) -> ack(xs',ack(Cons(x',xs'),xs))
ack(Nil(),n) -> Cons(Cons(Nil(),Nil()),n)
goal(m,n) -> ack(m,n)
- Signature:
{ack/2,goal/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {ack,goal} and constructors {Cons,Nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
ack(Cons(x,y),u){u -> Cons(z,u)} =
ack(Cons(x,y),Cons(z,u)) ->^+ ack(y,ack(Cons(x,y),u))
= C[ack(Cons(x,y),u) = ack(Cons(x,y),u){}]
WORST_CASE(Omega(n^1),?)