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