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:

merge(x, nil) → x
merge(nil, y) → y
merge(++(x, y), ++(u, v)) → ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) → ++(u, merge(++(x, y), v))

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
merge(++(x, y), ++(u, v)) →⁺ ++(x, merge(y, ++(u, v)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [y / ++(x, y)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)