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