The Runtime Complexity (full) 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:

plus(plus(X, Y), Z) → plus(X, plus(Y, Z))
times(X, s(Y)) → plus(X, times(Y, X))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
times(s(Y5_0), s(Y)) →⁺ plus(s(Y5_0), plus(Y, times(Y5_0, Y)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1].
The pumping substitution is [Y5_0 / s(Y5_0), Y / s(Y)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)