* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond(false(),x,y,z) -> 0()
cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
d(x,s(y),z) -> cond(ge(x,z),x,y,z)
div(x,s(y)) -> d(x,s(y),0())
ge(u,0()) -> true()
ge(0(),s(v)) -> false()
ge(s(u),s(v)) -> ge(u,v)
plus(n,0()) -> n
plus(n,s(m)) -> s(plus(n,m))
- Signature:
{cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,false,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond(false(),x,y,z) -> 0()
cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
d(x,s(y),z) -> cond(ge(x,z),x,y,z)
div(x,s(y)) -> d(x,s(y),0())
ge(u,0()) -> true()
ge(0(),s(v)) -> false()
ge(s(u),s(v)) -> ge(u,v)
plus(n,0()) -> n
plus(n,s(m)) -> s(plus(n,m))
- Signature:
{cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,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),?)