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