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