* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
cond2(false(),x,y) -> cond1(p(x),y)
cond2(true(),x,y) -> cond1(y,y)
gr(0(),x) -> false()
gr(s(x),0()) -> true()
gr(s(x),s(y)) -> gr(x,y)
neq(0(),0()) -> false()
neq(0(),s(x)) -> true()
neq(s(x),0()) -> true()
neq(s(x),s(y)) -> neq(x,y)
p(0()) -> 0()
p(s(x)) -> x
- Signature:
{cond1/2,cond2/3,gr/2,neq/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond1,cond2,gr,neq,p} 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:
cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
cond2(false(),x,y) -> cond1(p(x),y)
cond2(true(),x,y) -> cond1(y,y)
gr(0(),x) -> false()
gr(s(x),0()) -> true()
gr(s(x),s(y)) -> gr(x,y)
neq(0(),0()) -> false()
neq(0(),s(x)) -> true()
neq(s(x),0()) -> true()
neq(s(x),s(y)) -> neq(x,y)
p(0()) -> 0()
p(s(x)) -> x
- Signature:
{cond1/2,cond2/3,gr/2,neq/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond1,cond2,gr,neq,p} and constructors {0,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
gr(x,y){x -> s(x),y -> s(y)} =
gr(s(x),s(y)) ->^+ gr(x,y)
= C[gr(x,y) = gr(x,y){}]
WORST_CASE(Omega(n^1),?)