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