* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
and(x,false()) -> false()
and(x,true()) -> x
f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
gt(0(),v) -> false()
gt(s(u),0()) -> true()
gt(s(u),s(v)) -> gt(u,v)
- Signature:
{and/2,f/4,gt/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,f,gt} 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
f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
gt(0(),v) -> false()
gt(s(u),0()) -> true()
gt(s(u),s(v)) -> gt(u,v)
- Signature:
{and/2,f/4,gt/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,f,gt} 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),?)