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