* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
0() -> n__0()
activate(X) -> X
activate(n__0()) -> 0()
activate(n__adx(X)) -> adx(activate(X))
activate(n__incr(X)) -> incr(activate(X))
activate(n__s(X)) -> s(X)
activate(n__zeros()) -> zeros()
adx(X) -> n__adx(X)
adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
hd(cons(X,Y)) -> activate(X)
incr(X) -> n__incr(X)
incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
nats() -> adx(zeros())
s(X) -> n__s(X)
tl(cons(X,Y)) -> activate(Y)
zeros() -> cons(n__0(),n__zeros())
zeros() -> n__zeros()
- Signature:
{0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1
,n__zeros/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl
,zeros} and constructors {cons,n__0,n__adx,n__incr,n__s,n__zeros}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
0() -> n__0()
activate(X) -> X
activate(n__0()) -> 0()
activate(n__adx(X)) -> adx(activate(X))
activate(n__incr(X)) -> incr(activate(X))
activate(n__s(X)) -> s(X)
activate(n__zeros()) -> zeros()
adx(X) -> n__adx(X)
adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
hd(cons(X,Y)) -> activate(X)
incr(X) -> n__incr(X)
incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
nats() -> adx(zeros())
s(X) -> n__s(X)
tl(cons(X,Y)) -> activate(Y)
zeros() -> cons(n__0(),n__zeros())
zeros() -> n__zeros()
- Signature:
{0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1
,n__zeros/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl
,zeros} and constructors {cons,n__0,n__adx,n__incr,n__s,n__zeros}
+ 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),?)