* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
filter(cons(X,Y),0(),M) -> cons(0(),filter(Y,M,M))
filter(cons(X,Y),s(N),M) -> cons(X,filter(Y,N,M))
nats(N) -> cons(N,nats(s(N)))
sieve(cons(0(),Y)) -> cons(0(),sieve(Y))
sieve(cons(s(N),Y)) -> cons(s(N),sieve(filter(Y,N,N)))
zprimes() -> sieve(nats(s(s(0()))))
- Signature:
{filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
filter(cons(X,Y),0(),M) -> cons(0(),filter(Y,M,M))
filter(cons(X,Y),s(N),M) -> cons(X,filter(Y,N,M))
nats(N) -> cons(N,nats(s(N)))
sieve(cons(0(),Y)) -> cons(0(),sieve(Y))
sieve(cons(s(N),Y)) -> cons(s(N),sieve(filter(Y,N,N)))
zprimes() -> sieve(nats(s(s(0()))))
- Signature:
{filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
filter(y,z,u){y -> cons(x,y),z -> s(z)} =
filter(cons(x,y),s(z),u) ->^+ cons(x,filter(y,z,u))
= C[filter(y,z,u) = filter(y,z,u){}]
WORST_CASE(Omega(n^1),?)