* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
if(false(),c,x,y,z) -> z
if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
le(0(),x) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
len(cons(x,xs)) -> s(len(xs))
len(nil()) -> 0()
min(0(),y) -> 0()
min(s(x),0()) -> 0()
min(s(x),s(y)) -> min(x,y)
sum(x,0()) -> x
sum(x,s(y)) -> s(sum(x,y))
take(0(),cons(y,ys)) -> y
take(s(x),cons(y,ys)) -> take(x,ys)
- Signature:
{addList/2,if/5,le/2,len/1,min/2,sum/2,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {addList,if,le,len,min,sum,take} and constructors {0,cons
,false,nil,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
if(false(),c,x,y,z) -> z
if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
le(0(),x) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
len(cons(x,xs)) -> s(len(xs))
len(nil()) -> 0()
min(0(),y) -> 0()
min(s(x),0()) -> 0()
min(s(x),s(y)) -> min(x,y)
sum(x,0()) -> x
sum(x,s(y)) -> s(sum(x,y))
take(0(),cons(y,ys)) -> y
take(s(x),cons(y,ys)) -> take(x,ys)
- Signature:
{addList/2,if/5,le/2,len/1,min/2,sum/2,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {addList,if,le,len,min,sum,take} and constructors {0,cons
,false,nil,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
le(x,y){x -> s(x),y -> s(y)} =
le(s(x),s(y)) ->^+ le(x,y)
= C[le(x,y) = le(x,y){}]
WORST_CASE(Omega(n^1),?)