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:

f(X) → if(X, c, f(true))
if(true, X, Y) → X
if(false, X, Y) → Y

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(X) →⁺ if(X, c, f(true))
gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
The pumping substitution is [ ].
The result substitution is [X / true].

(2) BOUNDS(INF, INF)