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__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: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
mark(2nd(from(X2701_0))) →⁺ a__2nd(cons(mark(mark(X2701_0)), from(s(mark(X2701_0)))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0].
The pumping substitution is [X2701_0 / 2nd(from(X2701_0))].
The result substitution is [ ].

The rewrite sequence
mark(2nd(from(X2701_0))) →⁺ a__2nd(cons(mark(mark(X2701_0)), from(s(mark(X2701_0)))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0,0].
The pumping substitution is [X2701_0 / 2nd(from(X2701_0))].
The result substitution is [ ].

(2) BOUNDS(2^n, INF)