* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
activate(n__from(X)) -> from(activate(X))
activate(n__nil()) -> nil()
activate(n__s(X)) -> s(activate(X))
cons(X1,X2) -> n__cons(X1,X2)
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
length(n__cons(X,Y)) -> s(length1(activate(Y)))
length(n__nil()) -> 0()
length1(X) -> length(activate(X))
nil() -> n__nil()
s(X) -> n__s(X)
- Signature:
{activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1,nil
,s} and constructors {0,n__cons,n__from,n__nil,n__s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
activate(n__from(X)) -> from(activate(X))
activate(n__nil()) -> nil()
activate(n__s(X)) -> s(activate(X))
cons(X1,X2) -> n__cons(X1,X2)
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
length(n__cons(X,Y)) -> s(length1(activate(Y)))
length(n__nil()) -> 0()
length1(X) -> length(activate(X))
nil() -> n__nil()
s(X) -> n__s(X)
- Signature:
{activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1,nil
,s} and constructors {0,n__cons,n__from,n__nil,n__s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
activate(x){x -> n__cons(x,y)} =
activate(n__cons(x,y)) ->^+ cons(activate(x),y)
= C[activate(x) = activate(x){}]
WORST_CASE(Omega(n^1),?)