* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
r(xs,ys,zs,nil()) -> xs
r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
- Signature:
{r/4} / {cons/2,nil/0,succ/1,zero/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
r(xs,ys,zs,nil()) -> xs
r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws)))
r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws)
r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws)
- Signature:
{r/4} / {cons/2,nil/0,succ/1,zero/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
r(x,cons(y,z),v,cons(w,x_6)){v -> cons(u,v)} =
r(x,cons(y,z),cons(u,v),cons(w,x_6)) ->^+ r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6)))
= C[r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6))) = r(x,cons(y,z),v,cons(w,x_6)){x -> z
,w -> succ(zero())
,x_6 -> cons(w,x_6)}]
WORST_CASE(Omega(n^1),?)