* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
++(.(x,y),z) -> .(x,++(y,z))
++(nil(),y) -> y
if(false(),x,y) -> x
if(true(),x,y) -> x
merge(x,nil()) -> x
merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
merge(nil(),y) -> y
- Signature:
{++/2,if/3,merge/2} / {./2,2,false/0,nil/0,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {++,if,merge} and constructors {.,<,false,nil,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
++(.(x,y),z) -> .(x,++(y,z))
++(nil(),y) -> y
if(false(),x,y) -> x
if(true(),x,y) -> x
merge(x,nil()) -> x
merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
merge(nil(),y) -> y
- Signature:
{++/2,if/3,merge/2} / {./2,2,false/0,nil/0,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {++,if,merge} and constructors {.,<,false,nil,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
++(y,z){y -> .(x,y)} =
++(.(x,y),z) ->^+ .(x,++(y,z))
= C[++(y,z) = ++(y,z){}]
WORST_CASE(Omega(n^1),?)