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:

f(c(X, s(Y))) → f(c(s(X), Y))
g(c(s(X), Y)) → f(c(X, s(Y)))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

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

(2) BOUNDS(n^1, INF)