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