* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
*(x,0()) -> 0()
*(x,s(y)) -> +(x,*(x,y))
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
f(s(x)) -> f(-(max(*(s(x),s(x)),+(s(x),s(s(s(0()))))),max(s(*(s(x),s(x))),+(s(x),s(s(s(s(0()))))))))
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(x,y))
min(x,0()) -> 0()
min(0(),y) -> 0()
min(s(x),s(y)) -> s(min(x,y))
- Signature:
{*/2,+/2,-/2,f/1,max/2,min/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {*,+,-,f,max,min} 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,*(x,y))
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
f(s(x)) -> f(-(max(*(s(x),s(x)),+(s(x),s(s(s(0()))))),max(s(*(s(x),s(x))),+(s(x),s(s(s(s(0()))))))))
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(x,y))
min(x,0()) -> 0()
min(0(),y) -> 0()
min(s(x),s(y)) -> s(min(x,y))
- Signature:
{*/2,+/2,-/2,f/1,max/2,min/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {*,+,-,f,max,min} 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,*(x,y))
= C[*(x,y) = *(x,y){}]
WORST_CASE(Omega(n^1),?)