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