* Step 1: Sum WORST_CASE(NON_POLY,?)
+ Considered Problem:
- Strict TRS:
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
fib(0()) -> 0()
fib(s(0())) -> s(0())
fib(s(s(x))) -> +(fib(s(x)),fib(x))
- Signature:
{+/2,fib/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,fib} and constructors {0,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(NON_POLY,?)
+ Considered Problem:
- Strict TRS:
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
fib(0()) -> 0()
fib(s(0())) -> s(0())
fib(s(s(x))) -> +(fib(s(x)),fib(x))
- Signature:
{+/2,fib/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,fib} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
fib(s(x)){x -> s(x)} =
fib(s(s(x))) ->^+ +(fib(s(x)),fib(x))
= C[fib(s(x)) = fib(s(x)){}]
fib(x){x -> s(s(x))} =
fib(s(s(x))) ->^+ +(fib(s(x)),fib(x))
= C[fib(x) = fib(x){}]
WORST_CASE(NON_POLY,?)