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