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:

a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
a__2nd(cons(X, cons(2nd(cons(X118_0, X219_0)), Z))) →⁺ a__2nd(cons(mark(X118_0), X219_0))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [X219_0 / cons(2nd(cons(X118_0, X219_0)), Z)].
The result substitution is [X / mark(X118_0)].

(2) BOUNDS(n^1, INF)