The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) Obligation:

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

f(n__a, X, X) → f(activate(X), b, n__b)
b → a
a → n__a
b → n__b
activate(n__a) → a
activate(n__b) → b
activate(X) → X

Rewrite Strategy: INNERMOST

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(n__a, n__b, n__b) →⁺ f(n__a, n__b, n__b)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [ ].

(2) BOUNDS(INF, INF)