* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
rev(nil()) -> nil()
rev1(x,++(y,z)) -> rev1(y,z)
rev1(x,nil()) -> x
rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
rev2(x,nil()) -> nil()
- Signature:
{rev/1,rev1/2,rev2/2} / {++/2,nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {++,nil}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
rev(nil()) -> nil()
rev1(x,++(y,z)) -> rev1(y,z)
rev1(x,nil()) -> x
rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
rev2(x,nil()) -> nil()
- Signature:
{rev/1,rev1/2,rev2/2} / {++/2,nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {++,nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
rev1(x,z){z -> ++(y,z)} =
rev1(x,++(y,z)) ->^+ rev1(y,z)
= C[rev1(y,z) = rev1(x,z){x -> y}]
WORST_CASE(Omega(n^1),?)