* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
and(x,false()) -> false()
and(x,true()) -> x
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
gt(0(),v) -> false()
gt(s(u),0()) -> true()
gt(s(u),s(v)) -> gt(u,v)
plus(n,0()) -> n
plus(n,s(m)) -> s(plus(n,m))
- Signature:
{and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,double,f,gt,plus} and constructors {0,false,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
and(x,false()) -> false()
and(x,true()) -> x
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
gt(0(),v) -> false()
gt(s(u),0()) -> true()
gt(s(u),s(v)) -> gt(u,v)
plus(n,0()) -> n
plus(n,s(m)) -> s(plus(n,m))
- Signature:
{and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,double,f,gt,plus} and constructors {0,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
double(x){x -> s(x)} =
double(s(x)) ->^+ s(s(double(x)))
= C[double(x) = double(x){}]
WORST_CASE(Omega(n^1),?)