* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__incr(X)) -> incr(activate(X))
activate(n__nats()) -> nats()
activate(n__odds()) -> odds()
head(cons(X,XS)) -> X
incr(X) -> n__incr(X)
incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
nats() -> cons(0(),n__incr(n__nats()))
nats() -> n__nats()
odds() -> incr(pairs())
odds() -> n__odds()
pairs() -> cons(0(),n__incr(n__odds()))
tail(cons(X,XS)) -> activate(XS)
- Signature:
{activate/1,head/1,incr/1,nats/0,odds/0,pairs/0,tail/1} / {0/0,cons/2,n__incr/1,n__nats/0,n__odds/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,head,incr,nats,odds,pairs
,tail} and constructors {0,cons,n__incr,n__nats,n__odds,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__incr(X)) -> incr(activate(X))
activate(n__nats()) -> nats()
activate(n__odds()) -> odds()
head(cons(X,XS)) -> X
incr(X) -> n__incr(X)
incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
nats() -> cons(0(),n__incr(n__nats()))
nats() -> n__nats()
odds() -> incr(pairs())
odds() -> n__odds()
pairs() -> cons(0(),n__incr(n__odds()))
tail(cons(X,XS)) -> activate(XS)
- Signature:
{activate/1,head/1,incr/1,nats/0,odds/0,pairs/0,tail/1} / {0/0,cons/2,n__incr/1,n__nats/0,n__odds/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,head,incr,nats,odds,pairs
,tail} and constructors {0,cons,n__incr,n__nats,n__odds,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
activate(x){x -> n__incr(x)} =
activate(n__incr(x)) ->^+ incr(activate(x))
= C[activate(x) = activate(x){}]
WORST_CASE(Omega(n^1),?)