* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
if(true(),x,y,z,u) -> u
if2(false(),x,y,z,u) -> modIter(x,y,z,u)
if2(true(),x,y,z,u) -> modIter(x,y,z,0())
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
mod(x,0()) -> modZeroErro()
mod(x,s(y)) -> modIter(x,s(y),0(),0())
modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
- Signature:
{if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false
,modZeroErro,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u))
if(true(),x,y,z,u) -> u
if2(false(),x,y,z,u) -> modIter(x,y,z,u)
if2(true(),x,y,z,u) -> modIter(x,y,z,0())
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
mod(x,0()) -> modZeroErro()
mod(x,s(y)) -> modIter(x,s(y),0(),0())
modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u)
- Signature:
{if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false
,modZeroErro,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
le(x,y){x -> s(x),y -> s(y)} =
le(s(x),s(y)) ->^+ le(x,y)
= C[le(x,y) = le(x,y){}]
WORST_CASE(Omega(n^1),?)