* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
check(free(x)) -> free(check(x))
check(new(x)) -> new(check(x))
check(old(x)) -> old(x)
check(old(x)) -> old(check(x))
new(free(x)) -> free(new(x))
new(serve()) -> free(serve())
old(free(x)) -> free(old(x))
old(serve()) -> free(serve())
top1(free(x),y) -> top2(x,check(new(y)))
top1(free(x),y) -> top2(check(x),new(y))
top1(free(x),y) -> top2(check(new(x)),y)
top1(free(x),y) -> top2(new(x),check(y))
top2(x,free(y)) -> top1(x,check(new(y)))
top2(x,free(y)) -> top1(check(x),new(y))
top2(x,free(y)) -> top1(check(new(x)),y)
top2(x,free(y)) -> top1(new(x),check(y))
- Signature:
{check/1,new/1,old/1,top1/2,top2/2} / {free/1,serve/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {check,new,old,top1,top2} and constructors {free,serve}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
check(free(x)) -> free(check(x))
check(new(x)) -> new(check(x))
check(old(x)) -> old(x)
check(old(x)) -> old(check(x))
new(free(x)) -> free(new(x))
new(serve()) -> free(serve())
old(free(x)) -> free(old(x))
old(serve()) -> free(serve())
top1(free(x),y) -> top2(x,check(new(y)))
top1(free(x),y) -> top2(check(x),new(y))
top1(free(x),y) -> top2(check(new(x)),y)
top1(free(x),y) -> top2(new(x),check(y))
top2(x,free(y)) -> top1(x,check(new(y)))
top2(x,free(y)) -> top1(check(x),new(y))
top2(x,free(y)) -> top1(check(new(x)),y)
top2(x,free(y)) -> top1(new(x),check(y))
- Signature:
{check/1,new/1,old/1,top1/2,top2/2} / {free/1,serve/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {check,new,old,top1,top2} and constructors {free,serve}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
check(x){x -> free(x)} =
check(free(x)) ->^+ free(check(x))
= C[check(x) = check(x){}]
WORST_CASE(Omega(n^1),?)