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__f(g(X), Y) → a__f(mark(X), f(g(X), Y))
mark(f(X1, X2)) → a__f(mark(X1), X2)
mark(g(X)) → g(mark(X))
a__f(X1, X2) → f(X1, X2)

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
mark(f(g(X2938_0), X2)) →⁺ a__f(mark(mark(X2938_0)), f(g(mark(X2938_0)), X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [X2938_0 / f(g(X2938_0), X2)].
The result substitution is [ ].

The rewrite sequence
mark(f(g(X2938_0), X2)) →⁺ a__f(mark(mark(X2938_0)), f(g(mark(X2938_0)), X2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
The pumping substitution is [X2938_0 / f(g(X2938_0), X2)].
The result substitution is [ ].

(2) BOUNDS(2^n, INF)