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