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