The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

anchored(Cons(x, xs), y) → anchored(xs, Cons(Cons(Nil, Nil), y))
anchored(Nil, y) → y
goal(x, y) → anchored(x, y)

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:

anchored(Cons(x, xs), y) → anchored(xs, Cons(Cons(Nil, Nil), y))
anchored(Nil, y) → y
goal(x, y) → anchored(x, y)

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:

anchored(Cons(xs), y) → anchored(xs, Cons(y))
anchored(Nil, y) → y
goal(x, y) → anchored(x, y)

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
anchored(Cons(xs), y) →⁺ anchored(xs, Cons(y))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [xs / Cons(xs)].
The result substitution is [y / Cons(y)].

(6) BOUNDS(n^1, INF)