* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
fib(x) -> fibiter(x,0(),0(),s(0()))
fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y)
if(false(),b,c,x,y) -> x
if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y))
lt(x,0()) -> false()
lt(0(),s(y)) -> true()
lt(s(x),s(y)) -> lt(x,y)
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
- Signature:
{fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} 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:
fib(x) -> fibiter(x,0(),0(),s(0()))
fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y)
if(false(),b,c,x,y) -> x
if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y))
lt(x,0()) -> false()
lt(0(),s(y)) -> true()
lt(s(x),s(y)) -> lt(x,y)
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
- Signature:
{fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} 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),?)