The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(2^n, INF).

(0) Obligation:

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

a__first(0, X) → nil
a__first(s(X), cons(Y, Z)) → cons(mark(Y), first(X, Z))
a__from(X) → cons(mark(X), from(s(X)))
mark(first(X1, X2)) → a__first(mark(X1), mark(X2))
mark(from(X)) → a__from(mark(X))
mark(0) → 0
mark(nil) → nil
mark(s(X)) → s(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
a__first(X1, X2) → first(X1, X2)
a__from(X) → from(X)

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
mark(first(from(X7148_3), X2)) →⁺ a__first(cons(mark(mark(X7148_3)), from(s(mark(X7148_3)))), mark(X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0].
The pumping substitution is [X7148_3 / first(from(X7148_3), X2)].
The result substitution is [ ].

The rewrite sequence
mark(first(from(X7148_3), X2)) →⁺ a__first(cons(mark(mark(X7148_3)), from(s(mark(X7148_3)))), mark(X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0,0].
The pumping substitution is [X7148_3 / first(from(X7148_3), X2)].
The result substitution is [ ].

(2) BOUNDS(2^n, INF)