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