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