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