* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
2nd(cons(X,XS)) -> head(XS)
from(X) -> cons(X,from(s(X)))
head(cons(X,XS)) -> X
sel(0(),cons(X,XS)) -> X
sel(s(N),cons(X,XS)) -> sel(N,XS)
take(0(),XS) -> nil()
take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
- Signature:
{2nd/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,nil/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {2nd,from,head,sel,take} and constructors {0,cons,nil,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
2nd(cons(X,XS)) -> head(XS)
from(X) -> cons(X,from(s(X)))
head(cons(X,XS)) -> X
sel(0(),cons(X,XS)) -> X
sel(s(N),cons(X,XS)) -> sel(N,XS)
take(0(),XS) -> nil()
take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
- Signature:
{2nd/1,from/1,head/1,sel/2,take/2} / {0/0,cons/2,nil/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {2nd,from,head,sel,take} and constructors {0,cons,nil,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
sel(x,z){x -> s(x),z -> cons(y,z)} =
sel(s(x),cons(y,z)) ->^+ sel(x,z)
= C[sel(x,z) = sel(x,z){}]
WORST_CASE(Omega(n^1),?)