(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
naiverev(Cons(x, xs)) → app(naiverev(xs), Cons(x, Nil))
app(Cons(x, xs), ys) → Cons(x, app(xs, ys))
notEmpty(Cons(x, xs)) → True
notEmpty(Nil) → False
naiverev(Nil) → Nil
app(Nil, ys) → ys
goal(xs) → naiverev(xs)
Rewrite Strategy: INNERMOST
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
naiverev(Cons(x, xs)) → app(naiverev(xs), Cons(x, Nil))
app(Cons(x, xs), ys) → Cons(x, app(xs, ys))
notEmpty(Cons(x, xs)) → True
notEmpty(Nil) → False
naiverev(Nil) → Nil
app(Nil, ys) → ys
goal(xs) → naiverev(xs)
S is empty.
Rewrite Strategy: INNERMOST
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
Cons/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
naiverev(Cons(xs)) → app(naiverev(xs), Cons(Nil))
app(Cons(xs), ys) → Cons(app(xs, ys))
notEmpty(Cons(xs)) → True
notEmpty(Nil) → False
naiverev(Nil) → Nil
app(Nil, ys) → ys
goal(xs) → naiverev(xs)
S is empty.
Rewrite Strategy: INNERMOST
(5) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
naiverev(Cons(xs)) →+ app(naiverev(xs), Cons(Nil))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [xs / Cons(xs)].
The result substitution is [ ].
(6) BOUNDS(n^1, INF)