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