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