* 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(x,y),s(y)))
f(x,0(),b) -> x
f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
minus(x,x) -> 0()
minus(x,0()) -> x
minus(0(),x) -> 0()
minus(s(x),s(y)) -> minus(x,y)
- Signature:
{div/2,f/3,minus/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,f,minus} 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(x,y),s(y)))
f(x,0(),b) -> x
f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
minus(x,x) -> 0()
minus(x,0()) -> x
minus(0(),x) -> 0()
minus(s(x),s(y)) -> minus(x,y)
- Signature:
{div/2,f/3,minus/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,f,minus} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
minus(x,y){x -> s(x),y -> s(y)} =
minus(s(x),s(y)) ->^+ minus(x,y)
= C[minus(x,y) = minus(x,y){}]
WORST_CASE(Omega(n^1),?)