* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
and(x,false()) -> false()
and(false(),x) -> false()
and(true(),true()) -> true()
cond1(true(),x,y) -> cond2(gr(x,y),x,y)
cond2(false(),x,y) -> cond4(gr(y,0()),x,y)
cond2(true(),x,y) -> cond3(gr(x,0()),x,y)
cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y)
cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y))
gr(0(),x) -> false()
gr(s(x),0()) -> true()
gr(s(x),s(y)) -> gr(x,y)
p(0()) -> 0()
p(s(x)) -> x
- Signature:
{and/2,cond1/3,cond2/3,cond3/3,cond4/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,cond1,cond2,cond3,cond4,gr,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:
and(x,false()) -> false()
and(false(),x) -> false()
and(true(),true()) -> true()
cond1(true(),x,y) -> cond2(gr(x,y),x,y)
cond2(false(),x,y) -> cond4(gr(y,0()),x,y)
cond2(true(),x,y) -> cond3(gr(x,0()),x,y)
cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y)
cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y)
cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y))
gr(0(),x) -> false()
gr(s(x),0()) -> true()
gr(s(x),s(y)) -> gr(x,y)
p(0()) -> 0()
p(s(x)) -> x
- Signature:
{and/2,cond1/3,cond2/3,cond3/3,cond4/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {and,cond1,cond2,cond3,cond4,gr,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),?)