The Runtime Complexity (full) 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:

c → f(g(c))
f(g(X)) → g(X)

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
c →⁺ f(g(c))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [ ].
The result substitution is [ ].

(2) BOUNDS(INF, INF)