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