* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
if(false(),x,y,z) -> loop(x,double(y),s(z))
if(true(),x,y,z) -> z
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
log(0()) -> logError()
log(s(x)) -> loop(s(x),s(0()),0())
loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
- Signature:
{double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError
,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
if(false(),x,y,z) -> loop(x,double(y),s(z))
if(true(),x,y,z) -> z
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
log(0()) -> logError()
log(s(x)) -> loop(s(x),s(0()),0())
loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
- Signature:
{double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError
,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
double(x){x -> s(x)} =
double(s(x)) ->^+ s(s(double(x)))
= C[double(x) = double(x){}]
WORST_CASE(Omega(n^1),?)