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