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