* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v)
if(true(),x,y,z,u,v) -> v
if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v)
if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v))
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
quot(x,0()) -> quotZeroErro()
quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0())
quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v)
- Signature:
{if/6,if2/6,le/2,quot/2,quotIter/5} / {0/0,false/0,quotZeroErro/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {if,if2,le,quot,quotIter} and constructors {0,false
,quotZeroErro,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,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v)
if(true(),x,y,z,u,v) -> v
if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v)
if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v))
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
quot(x,0()) -> quotZeroErro()
quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0())
quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v)
- Signature:
{if/6,if2/6,le/2,quot/2,quotIter/5} / {0/0,false/0,quotZeroErro/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {if,if2,le,quot,quotIter} and constructors {0,false
,quotZeroErro,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),?)