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