* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
div(x,y) -> ify(ge(y,s(0())),x,y)
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
if(false(),x,y) -> 0()
if(true(),x,y) -> s(div(minus(x,y),y))
ify(false(),x,y) -> divByZeroError()
ify(true(),x,y) -> if(ge(x,y),x,y)
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
- Signature:
{div/2,ge/2,if/3,ify/3,minus/2} / {0/0,divByZeroError/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,ge,if,ify,minus} and constructors {0,divByZeroError
,false,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
div(x,y) -> ify(ge(y,s(0())),x,y)
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
if(false(),x,y) -> 0()
if(true(),x,y) -> s(div(minus(x,y),y))
ify(false(),x,y) -> divByZeroError()
ify(true(),x,y) -> if(ge(x,y),x,y)
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
- Signature:
{div/2,ge/2,if/3,ify/3,minus/2} / {0/0,divByZeroError/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,ge,if,ify,minus} and constructors {0,divByZeroError
,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
ge(x,y){x -> s(x),y -> s(y)} =
ge(s(x),s(y)) ->^+ ge(x,y)
= C[ge(x,y) = ge(x,y){}]
WORST_CASE(Omega(n^1),?)