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:

duplicate(Cons(x, xs)) → Cons(x, Cons(x, duplicate(xs)))
duplicate(Nil) → Nil
goal(x) → duplicate(x)

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:

duplicate(Cons(x, xs)) → Cons(x, Cons(x, duplicate(xs)))
duplicate(Nil) → Nil
goal(x) → duplicate(x)

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:

duplicate(Cons(xs)) → Cons(Cons(duplicate(xs)))
duplicate(Nil) → Nil
goal(x) → duplicate(x)

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
duplicate(Cons(xs)) →⁺ Cons(Cons(duplicate(xs)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [xs / Cons(xs)].
The result substitution is [ ].

(6) BOUNDS(n^1, INF)