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